Functions averages over the roots of unity, cauchy problems and addition formulas

An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to deri...

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Bibliographic Details
Published inComplex variables, theory & application Vol. 49; no. 11; pp. 807 - 820
Main Author Bragg, L.R.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 15.09.2004
Subjects
addition formulas and integral representations
AMS Subject Classifications: Primary 30E99
Averaging operator
Cauchy problems
Hadamard product
hypergeometric functions
idempotent
Secondary 30E20
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ISSN0278-1077
1563-5066
DOI10.1080/02781070412331298570

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Summary:An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions.
ISSN:0278-1077
1563-5066
DOI:10.1080/02781070412331298570