Asymptotic expansions for the alternating Hurwitz zeta function and its derivatives
LetζE(s,q)=∑n=0∞(−1)n(n+q)s be the alternating Hurwitz (or Hurwitz-type Euler) zeta function. In this paper, we obtain the following asymptotic expansion of ζE(s,q)ζE(s,q)∼12q−s+14sq−s−1−12q−s∑k=1∞E2k+1(0)(2k+1)!(s)2k+1q2k+1, as |q|→∞, where E2k+1(0) are the special values of odd-order Euler polynom...
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| Published in | Journal of mathematical analysis and applications Vol. 537; no. 1; p. 128306 |
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| Format | Journal Article |
| Language | English |
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| Abstract | LetζE(s,q)=∑n=0∞(−1)n(n+q)s be the alternating Hurwitz (or Hurwitz-type Euler) zeta function.
In this paper, we obtain the following asymptotic expansion of ζE(s,q)ζE(s,q)∼12q−s+14sq−s−1−12q−s∑k=1∞E2k+1(0)(2k+1)!(s)2k+1q2k+1, as |q|→∞, where E2k+1(0) are the special values of odd-order Euler polynomials at 0, and we also consider representations and bounds for the remainder of the above asymptotic expansion. In addition, we derive the asymptotic expansions for the higher order derivatives of ζE(s,q) with respect to its first argumentζE(m)(s,q)≡∂m∂smζE(s,q), as |q|→∞. Finally, we also prove a new exact series representation of ζE(s,q). |
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| AbstractList | LetζE(s,q)=∑n=0∞(−1)n(n+q)s be the alternating Hurwitz (or Hurwitz-type Euler) zeta function.
In this paper, we obtain the following asymptotic expansion of ζE(s,q)ζE(s,q)∼12q−s+14sq−s−1−12q−s∑k=1∞E2k+1(0)(2k+1)!(s)2k+1q2k+1, as |q|→∞, where E2k+1(0) are the special values of odd-order Euler polynomials at 0, and we also consider representations and bounds for the remainder of the above asymptotic expansion. In addition, we derive the asymptotic expansions for the higher order derivatives of ζE(s,q) with respect to its first argumentζE(m)(s,q)≡∂m∂smζE(s,q), as |q|→∞. Finally, we also prove a new exact series representation of ζE(s,q). |
| ArticleNumber | 128306 |
| Author | Hu, Su Kim, Min-Soo |
| Author_xml | – sequence: 1 givenname: Su surname: Hu fullname: Hu, Su email: mahusu@scut.edu.cn organization: Department of Mathematics, South China University of Technology, Guangzhou 510640, China – sequence: 2 givenname: Min-Soo orcidid: 0000-0002-1867-0817 surname: Kim fullname: Kim, Min-Soo email: mskim@kyungnam.ac.kr organization: Department of Mathematics Education, Kyungnam University, Changwon, Gyeongnam 51767, Republic of Korea |
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| Cites_doi | 10.1016/j.jnt.2013.07.010 10.1080/00029890.1989.11972263 10.1080/10652469.2011.591393 10.1016/j.jmaa.2014.08.012 10.1016/j.jmaa.2021.125930 10.1016/j.jmaa.2019.123661 10.1016/j.cam.2007.05.009 10.1090/S0002-9939-1993-1172963-7 10.1007/s00009-022-02000-x 10.1080/10652469.2011.643627 10.1155/S0161171290000679 10.1016/j.jnt.2013.06.012 10.7153/jmi-09-81 10.3906/mat-1607-23 10.1016/j.jmaa.2019.05.061 10.1063/1.530072 10.1007/s10958-020-05131-2 10.1063/1.528986 10.1090/S0025-5718-1986-0842140-X 10.1016/j.jnt.2015.10.022 10.11650/twjm/1500406218 |
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| Keywords | Error bounds Asymptotic expansions Gamma function Euler polynomials Alternating Hurwitz zeta functions |
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| References | Hardy (br0210) 1949 Graham, Knuth, Patashnik (br0200) 1994 Chen, Paris (br0060) 2015; 250 Elezović (br0140) 2015; 9 Knopp (br0290) 1951 Elizalde (br0150) 1986; 47 Burić, Elezović (br0040) 2012; 23 Nemes (br0350) 2017; 473 Kostin, Sherstyukov (br0300) 2020; 251 Weil (br0450) 1984 Choi, Srivastava (br0080) 2011; 15 Coffey (br0110) 2008; 216 Can, Dağlı (br0100) 2017; 41 Hu, Kim (br0250) 2022; 509 Borwein, Borwein, Dilcher (br0030) 1989; 96 Ekera (br0130) Elizalde, Romeo (br0180) 1990; 13 Srivastava, Kurt, Simsek (br0430) 2012; 23 Kim, Hu (br0280) 2013; 133 Candelpergher (br0050) 2017; vol. 2185 (br0380) 2016 Hu, Kim, Kim (br0220) 2016; 162 Min (br0340) 2014; 134 Srivastava, Choi (br0420) 2012 Deninger (br0120) 1984; 351 Nörlund (br0370) 1924 Luke (br0320) 1969; vol. 53 Lampret (br0310) 2022; 19 Alzer, Choi (br0020) 2020; 484 Elizalde (br0160) 1993; 34 Hu, Kim, Kim (br0230) 2018; 55 Elizalde (br0170) 2012; vol. 855 Cohen (br0090) 2007; vol. 240 Kim (br0270) 2018; 42 Temme (br0440) 1996 NIST (br0360) Rudaz (br0390) 1990; 31 (br0010) 1972 Williams, Zhang (br0460) 1993; 119 Chen, Paris (br0070) Sun (br0410) Hu, Kim (br0240) 2019; 478 Wong (br0470) 2001; vol. 34 Erdélyi (br0190) 1956 Jordan (br0260) 1965 Magnus, Oberhettinger, Soni (br0330) 1966; vol. 52 Seri (br0400) 2015; 424 Borwein (10.1016/j.jmaa.2024.128306_br0030) 1989; 96 Hardy (10.1016/j.jmaa.2024.128306_br0210) 1949 Coffey (10.1016/j.jmaa.2024.128306_br0110) 2008; 216 Magnus (10.1016/j.jmaa.2024.128306_br0330) 1966; vol. 52 Williams (10.1016/j.jmaa.2024.128306_br0460) 1993; 119 Knopp (10.1016/j.jmaa.2024.128306_br0290) 1951 Chen (10.1016/j.jmaa.2024.128306_br0070) Hu (10.1016/j.jmaa.2024.128306_br0240) 2019; 478 Ekera (10.1016/j.jmaa.2024.128306_br0130) Elizalde (10.1016/j.jmaa.2024.128306_br0180) 1990; 13 Erdélyi (10.1016/j.jmaa.2024.128306_br0190) 1956 Kim (10.1016/j.jmaa.2024.128306_br0270) 2018; 42 NIST (10.1016/j.jmaa.2024.128306_br0360) Weil (10.1016/j.jmaa.2024.128306_br0450) 1984 Sun (10.1016/j.jmaa.2024.128306_br0410) Elizalde (10.1016/j.jmaa.2024.128306_br0170) 2012; vol. 855 (10.1016/j.jmaa.2024.128306_br0010) 1972 Min (10.1016/j.jmaa.2024.128306_br0340) 2014; 134 Srivastava (10.1016/j.jmaa.2024.128306_br0430) 2012; 23 Elizalde (10.1016/j.jmaa.2024.128306_br0150) 1986; 47 Kostin (10.1016/j.jmaa.2024.128306_br0300) 2020; 251 Cohen (10.1016/j.jmaa.2024.128306_br0090) 2007; vol. 240 Hu (10.1016/j.jmaa.2024.128306_br0220) 2016; 162 Alzer (10.1016/j.jmaa.2024.128306_br0020) 2020; 484 Choi (10.1016/j.jmaa.2024.128306_br0080) 2011; 15 Deninger (10.1016/j.jmaa.2024.128306_br0120) 1984; 351 Jordan (10.1016/j.jmaa.2024.128306_br0260) 1965 Luke (10.1016/j.jmaa.2024.128306_br0320) 1969; vol. 53 (10.1016/j.jmaa.2024.128306_br0380) 2016 Temme (10.1016/j.jmaa.2024.128306_br0440) 1996 Rudaz (10.1016/j.jmaa.2024.128306_br0390) 1990; 31 Chen (10.1016/j.jmaa.2024.128306_br0060) 2015; 250 Seri (10.1016/j.jmaa.2024.128306_br0400) 2015; 424 Hu (10.1016/j.jmaa.2024.128306_br0230) 2018; 55 Hu (10.1016/j.jmaa.2024.128306_br0250) 2022; 509 Lampret (10.1016/j.jmaa.2024.128306_br0310) 2022; 19 Srivastava (10.1016/j.jmaa.2024.128306_br0420) 2012 Wong (10.1016/j.jmaa.2024.128306_br0470) 2001; vol. 34 Nemes (10.1016/j.jmaa.2024.128306_br0350) 2017; 473 Graham (10.1016/j.jmaa.2024.128306_br0200) 1994 Elezović (10.1016/j.jmaa.2024.128306_br0140) 2015; 9 Candelpergher (10.1016/j.jmaa.2024.128306_br0050) 2017; vol. 2185 Can (10.1016/j.jmaa.2024.128306_br0100) 2017; 41 Nörlund (10.1016/j.jmaa.2024.128306_br0370) 1924 Burić (10.1016/j.jmaa.2024.128306_br0040) 2012; 23 Kim (10.1016/j.jmaa.2024.128306_br0280) 2013; 133 Elizalde (10.1016/j.jmaa.2024.128306_br0160) 1993; 34 |
| References_xml | – volume: 96 start-page: 681 year: 1989 end-page: 687 ident: br0030 article-title: Pi, Euler numbers, and asymptotic expansions publication-title: Am. Math. Mon. contributor: fullname: Dilcher – volume: vol. 34 year: 2001 ident: br0470 article-title: Asymptotic Approximations of Integrals publication-title: Classics in Applied Mathematics contributor: fullname: Wong – year: 1951 ident: br0290 article-title: Theory and Application of Infinite Series contributor: fullname: Knopp – volume: 23 start-page: 919 year: 2012 end-page: 938 ident: br0430 article-title: Some families of Genocchi type polynomials and their interpolation functions publication-title: Integral Transforms Spec. Funct. contributor: fullname: Simsek – volume: 19 year: 2022 ident: br0310 article-title: Simple derivation of the Euler-Boole type summation formula and examples of its use publication-title: Mediterr. J. Math. contributor: fullname: Lampret – year: 1996 ident: br0440 article-title: Special Functions, An Introduction to the Classical Functions of Mathematical Physics contributor: fullname: Temme – volume: 15 start-page: 501 year: 2011 end-page: 522 ident: br0080 article-title: The multiple Hurwitz zeta function and the multiple Hurwitz-Euler eta function publication-title: Taiwan. J. Math. contributor: fullname: Srivastava – volume: vol. 2185 year: 2017 ident: br0050 article-title: Ramanujan Summation of Divergent Series publication-title: Lecture Notes in Mathematics contributor: fullname: Candelpergher – year: 1956 ident: br0190 article-title: Asymptotic Expansions contributor: fullname: Erdélyi – year: 2016 ident: br0380 publication-title: 2014 NIST Digital Library of Mathematical Functions – volume: 509 year: 2022 ident: br0250 article-title: On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions publication-title: J. Math. Anal. Appl. contributor: fullname: Kim – year: 1984 ident: br0450 article-title: Number Theory, An Approach Through History, from Hammurapi to Legendre contributor: fullname: Weil – volume: 23 start-page: 355 year: 2012 end-page: 368 ident: br0040 article-title: New asymptotic expansions of the quotient of gamma functions publication-title: Integral Transforms Spec. Funct. contributor: fullname: Elezović – volume: 250 start-page: 514 year: 2015 end-page: 529 ident: br0060 article-title: Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function publication-title: Appl. Math. Comput. contributor: fullname: Paris – ident: br0070 article-title: Some results associated with Bernoulli and Euler numbers with applications contributor: fullname: Paris – volume: 34 start-page: 3222 year: 1993 end-page: 3226 ident: br0160 article-title: A simple recurrence for the higher derivatives of the Hurwitz zeta function publication-title: J. Math. Phys. contributor: fullname: Elizalde – volume: 134 start-page: 240 year: 2014 end-page: 257 ident: br0340 article-title: Zeros and special values of Witten zeta functions and Witten publication-title: J. Number Theory contributor: fullname: Min – volume: 162 start-page: 54 year: 2016 end-page: 67 ident: br0220 article-title: On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions publication-title: J. Number Theory contributor: fullname: Kim – volume: 119 start-page: 35 year: 1993 end-page: 49 ident: br0460 article-title: Special values of the Lerch zeta function and the evaluation of certain integrals publication-title: Proc. Am. Math. Soc. contributor: fullname: Zhang – year: 1965 ident: br0260 article-title: Calculus of Finite Differences contributor: fullname: Jordan – ident: br0360 article-title: Digital library of mathematical functions contributor: fullname: NIST – volume: vol. 240 year: 2007 ident: br0090 article-title: Number Theory Vol. II: Analytic and Modern Tools publication-title: Graduate Texts in Mathematics contributor: fullname: Cohen – volume: 133 start-page: 4233 year: 2013 end-page: 4250 ident: br0280 article-title: On publication-title: J. Number Theory contributor: fullname: Hu – volume: vol. 53 year: 1969 ident: br0320 article-title: The Special Functions and Their Approximations, Vol. I publication-title: Mathematics in Science and Engineering contributor: fullname: Luke – volume: 484 year: 2020 ident: br0020 article-title: Four parametric linear Euler sums publication-title: J. Math. Anal. Appl. contributor: fullname: Choi – volume: 42 start-page: 1166 year: 2018 end-page: 1179 ident: br0270 article-title: Some series involving the Euler zeta function publication-title: Turk. J. Math. contributor: fullname: Kim – volume: vol. 855 year: 2012 ident: br0170 article-title: Ten Physical Applications of Spectral Zeta Functions publication-title: Lecture Notes in Physics contributor: fullname: Elizalde – year: 1949 ident: br0210 article-title: Divergent Series contributor: fullname: Hardy – volume: 13 start-page: 453 year: 1990 end-page: 460 ident: br0180 article-title: An integral involving the generalized zeta function publication-title: Int. J. Math. Math. Sci. contributor: fullname: Romeo – volume: 473 year: 2017 ident: br0350 article-title: Error bounds for the asymptotic expansion of the Hurwitz zeta function publication-title: Proc. A. contributor: fullname: Nemes – year: 1972 ident: br0010 publication-title: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables – ident: br0410 article-title: Introduction to Bernoulli and Euler polynomials contributor: fullname: Sun – year: 2012 ident: br0420 article-title: Zeta and contributor: fullname: Choi – volume: 424 start-page: 826 year: 2015 end-page: 834 ident: br0400 article-title: A non-recursive formula for the higher derivatives of the Hurwitz zeta function publication-title: J. Math. Anal. Appl. contributor: fullname: Seri – year: 1994 ident: br0200 article-title: Concrete Mathematics contributor: fullname: Patashnik – volume: 55 start-page: 185 year: 2018 end-page: 210 ident: br0230 article-title: Special values and integral representations for the Hurwitz-type Euler zeta functions publication-title: J. Korean Math. Soc. contributor: fullname: Kim – ident: br0130 article-title: On the success probability of quantum order finding contributor: fullname: Ekera – volume: 251 start-page: 814 year: 2020 end-page: 838 ident: br0300 article-title: Asymptotic behavior of remainders of special number series publication-title: J. Math. Sci. (N.Y.) contributor: fullname: Sherstyukov – volume: 351 start-page: 171 year: 1984 end-page: 191 ident: br0120 article-title: On the analogue of the formula of Chowla and Selberg for real quadratic fields publication-title: J. Reine Angew. Math. contributor: fullname: Deninger – volume: 478 start-page: 952 year: 2019 end-page: 972 ident: br0240 article-title: On Dirichlet's lambda function publication-title: J. Math. Anal. Appl. contributor: fullname: Kim – volume: 31 start-page: 2832 year: 1990 end-page: 2834 ident: br0390 article-title: Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions publication-title: J. Math. Phys. contributor: fullname: Rudaz – volume: 41 start-page: 1204 year: 2017 end-page: 1223 ident: br0100 article-title: Character analogue of the Boole summation formula with applications publication-title: Turk. J. Math. contributor: fullname: Dağlı – year: 1924 ident: br0370 article-title: Vorlesungen über Differenzenrechnung contributor: fullname: Nörlund – volume: 216 start-page: 297 year: 2008 end-page: 305 ident: br0110 article-title: On some series representations of the Hurwitz zeta function publication-title: J. Comput. Appl. Math. contributor: fullname: Coffey – volume: 47 start-page: 347 year: 1986 end-page: 350 ident: br0150 article-title: An asymptotic expansion for the first derivative of the generalized Riemann zeta function publication-title: Math. Comput. contributor: fullname: Elizalde – volume: 9 start-page: 1001 year: 2015 end-page: 1054 ident: br0140 article-title: Asymptotic expansions of gamma and related functions, binomial coefficients, inequalities and means publication-title: J. Math. Inequal. contributor: fullname: Elezović – volume: vol. 52 year: 1966 ident: br0330 article-title: Formulas and Theorems for the Special Functions of Mathematical Physics publication-title: Die Grundlehren der mathematischen Wissenschaften contributor: fullname: Soni – volume: 351 start-page: 171 year: 1984 ident: 10.1016/j.jmaa.2024.128306_br0120 article-title: On the analogue of the formula of Chowla and Selberg for real quadratic fields publication-title: J. Reine Angew. Math. contributor: fullname: Deninger – volume: 134 start-page: 240 year: 2014 ident: 10.1016/j.jmaa.2024.128306_br0340 article-title: Zeros and special values of Witten zeta functions and Witten L-functions publication-title: J. Number Theory doi: 10.1016/j.jnt.2013.07.010 contributor: fullname: Min – volume: 96 start-page: 681 issue: 8 year: 1989 ident: 10.1016/j.jmaa.2024.128306_br0030 article-title: Pi, Euler numbers, and asymptotic expansions publication-title: Am. Math. Mon. doi: 10.1080/00029890.1989.11972263 contributor: fullname: Borwein – volume: 23 start-page: 355 issue: 5 year: 2012 ident: 10.1016/j.jmaa.2024.128306_br0040 article-title: New asymptotic expansions of the quotient of gamma functions publication-title: Integral Transforms Spec. Funct. doi: 10.1080/10652469.2011.591393 contributor: fullname: Burić – year: 1996 ident: 10.1016/j.jmaa.2024.128306_br0440 contributor: fullname: Temme – year: 1956 ident: 10.1016/j.jmaa.2024.128306_br0190 contributor: fullname: Erdélyi – volume: 424 start-page: 826 issue: 1 year: 2015 ident: 10.1016/j.jmaa.2024.128306_br0400 article-title: A non-recursive formula for the higher derivatives of the Hurwitz zeta function publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2014.08.012 contributor: fullname: Seri – year: 1972 ident: 10.1016/j.jmaa.2024.128306_br0010 – year: 2012 ident: 10.1016/j.jmaa.2024.128306_br0420 contributor: fullname: Srivastava – volume: vol. 855 year: 2012 ident: 10.1016/j.jmaa.2024.128306_br0170 article-title: Ten Physical Applications of Spectral Zeta Functions contributor: fullname: Elizalde – volume: 509 issue: 1 year: 2022 ident: 10.1016/j.jmaa.2024.128306_br0250 article-title: On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2021.125930 contributor: fullname: Hu – volume: vol. 52 year: 1966 ident: 10.1016/j.jmaa.2024.128306_br0330 article-title: Formulas and Theorems for the Special Functions of Mathematical Physics contributor: fullname: Magnus – volume: 484 issue: 1 year: 2020 ident: 10.1016/j.jmaa.2024.128306_br0020 article-title: Four parametric linear Euler sums publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2019.123661 contributor: fullname: Alzer – ident: 10.1016/j.jmaa.2024.128306_br0070 contributor: fullname: Chen – year: 1924 ident: 10.1016/j.jmaa.2024.128306_br0370 contributor: fullname: Nörlund – volume: 216 start-page: 297 issue: 1 year: 2008 ident: 10.1016/j.jmaa.2024.128306_br0110 article-title: On some series representations of the Hurwitz zeta function publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.05.009 contributor: fullname: Coffey – year: 1965 ident: 10.1016/j.jmaa.2024.128306_br0260 contributor: fullname: Jordan – volume: 119 start-page: 35 issue: 1 year: 1993 ident: 10.1016/j.jmaa.2024.128306_br0460 article-title: Special values of the Lerch zeta function and the evaluation of certain integrals publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1993-1172963-7 contributor: fullname: Williams – volume: 19 issue: 2 year: 2022 ident: 10.1016/j.jmaa.2024.128306_br0310 article-title: Simple derivation of the Euler-Boole type summation formula and examples of its use publication-title: Mediterr. J. Math. doi: 10.1007/s00009-022-02000-x contributor: fullname: Lampret – volume: 23 start-page: 919 issue: 12 year: 2012 ident: 10.1016/j.jmaa.2024.128306_br0430 article-title: Some families of Genocchi type polynomials and their interpolation functions publication-title: Integral Transforms Spec. Funct. doi: 10.1080/10652469.2011.643627 contributor: fullname: Srivastava – year: 2016 ident: 10.1016/j.jmaa.2024.128306_br0380 – volume: 13 start-page: 453 year: 1990 ident: 10.1016/j.jmaa.2024.128306_br0180 article-title: An integral involving the generalized zeta function publication-title: Int. J. Math. Math. Sci. doi: 10.1155/S0161171290000679 contributor: fullname: Elizalde – volume: 133 start-page: 4233 year: 2013 ident: 10.1016/j.jmaa.2024.128306_br0280 article-title: On p-adic diamond-Euler log gamma functions publication-title: J. Number Theory doi: 10.1016/j.jnt.2013.06.012 contributor: fullname: Kim – ident: 10.1016/j.jmaa.2024.128306_br0130 contributor: fullname: Ekera – ident: 10.1016/j.jmaa.2024.128306_br0410 contributor: fullname: Sun – volume: vol. 240 year: 2007 ident: 10.1016/j.jmaa.2024.128306_br0090 article-title: Number Theory Vol. II: Analytic and Modern Tools contributor: fullname: Cohen – volume: 9 start-page: 1001 issue: 4 year: 2015 ident: 10.1016/j.jmaa.2024.128306_br0140 article-title: Asymptotic expansions of gamma and related functions, binomial coefficients, inequalities and means publication-title: J. Math. Inequal. doi: 10.7153/jmi-09-81 contributor: fullname: Elezović – volume: 473 issue: 2203 year: 2017 ident: 10.1016/j.jmaa.2024.128306_br0350 article-title: Error bounds for the asymptotic expansion of the Hurwitz zeta function publication-title: Proc. A. contributor: fullname: Nemes – volume: 55 start-page: 185 issue: 1 year: 2018 ident: 10.1016/j.jmaa.2024.128306_br0230 article-title: Special values and integral representations for the Hurwitz-type Euler zeta functions publication-title: J. Korean Math. Soc. contributor: fullname: Hu – year: 1951 ident: 10.1016/j.jmaa.2024.128306_br0290 contributor: fullname: Knopp – volume: 250 start-page: 514 year: 2015 ident: 10.1016/j.jmaa.2024.128306_br0060 article-title: Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function publication-title: Appl. Math. Comput. contributor: fullname: Chen – volume: vol. 53 year: 1969 ident: 10.1016/j.jmaa.2024.128306_br0320 article-title: The Special Functions and Their Approximations, Vol. I contributor: fullname: Luke – year: 1984 ident: 10.1016/j.jmaa.2024.128306_br0450 contributor: fullname: Weil – volume: vol. 2185 year: 2017 ident: 10.1016/j.jmaa.2024.128306_br0050 article-title: Ramanujan Summation of Divergent Series contributor: fullname: Candelpergher – volume: 41 start-page: 1204 issue: 5 year: 2017 ident: 10.1016/j.jmaa.2024.128306_br0100 article-title: Character analogue of the Boole summation formula with applications publication-title: Turk. J. Math. doi: 10.3906/mat-1607-23 contributor: fullname: Can – volume: 478 start-page: 952 issue: 2 year: 2019 ident: 10.1016/j.jmaa.2024.128306_br0240 article-title: On Dirichlet's lambda function publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2019.05.061 contributor: fullname: Hu – volume: 42 start-page: 1166 issue: 3 year: 2018 ident: 10.1016/j.jmaa.2024.128306_br0270 article-title: Some series involving the Euler zeta function publication-title: Turk. J. Math. contributor: fullname: Kim – volume: 34 start-page: 3222 issue: 7 year: 1993 ident: 10.1016/j.jmaa.2024.128306_br0160 article-title: A simple recurrence for the higher derivatives of the Hurwitz zeta function publication-title: J. Math. Phys. doi: 10.1063/1.530072 contributor: fullname: Elizalde – year: 1994 ident: 10.1016/j.jmaa.2024.128306_br0200 contributor: fullname: Graham – volume: 251 start-page: 814 issue: 6 year: 2020 ident: 10.1016/j.jmaa.2024.128306_br0300 article-title: Asymptotic behavior of remainders of special number series publication-title: J. Math. Sci. (N.Y.) doi: 10.1007/s10958-020-05131-2 contributor: fullname: Kostin – year: 1949 ident: 10.1016/j.jmaa.2024.128306_br0210 contributor: fullname: Hardy – volume: 31 start-page: 2832 issue: 12 year: 1990 ident: 10.1016/j.jmaa.2024.128306_br0390 article-title: Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions publication-title: J. Math. Phys. doi: 10.1063/1.528986 contributor: fullname: Rudaz – volume: 47 start-page: 347 issue: 175 year: 1986 ident: 10.1016/j.jmaa.2024.128306_br0150 article-title: An asymptotic expansion for the first derivative of the generalized Riemann zeta function publication-title: Math. Comput. doi: 10.1090/S0025-5718-1986-0842140-X contributor: fullname: Elizalde – volume: 162 start-page: 54 year: 2016 ident: 10.1016/j.jmaa.2024.128306_br0220 article-title: On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions publication-title: J. Number Theory doi: 10.1016/j.jnt.2015.10.022 contributor: fullname: Hu – ident: 10.1016/j.jmaa.2024.128306_br0360 contributor: fullname: NIST – volume: 15 start-page: 501 issue: 2 year: 2011 ident: 10.1016/j.jmaa.2024.128306_br0080 article-title: The multiple Hurwitz zeta function and the multiple Hurwitz-Euler eta function publication-title: Taiwan. J. Math. doi: 10.11650/twjm/1500406218 contributor: fullname: Choi – volume: vol. 34 year: 2001 ident: 10.1016/j.jmaa.2024.128306_br0470 article-title: Asymptotic Approximations of Integrals contributor: fullname: Wong |
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| Snippet | LetζE(s,q)=∑n=0∞(−1)n(n+q)s be the alternating Hurwitz (or Hurwitz-type Euler) zeta function.
In this paper, we obtain the following asymptotic expansion of... |
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| SubjectTerms | Alternating Hurwitz zeta functions Asymptotic expansions Error bounds Euler polynomials Gamma function |
| Title | Asymptotic expansions for the alternating Hurwitz zeta function and its derivatives |
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