On bounds for solutions of monotonic first order difference-differential systems

• Published in: Journal of inequalities and applications Vol. 2012; no. 1; pp. 1 - 65
• Main Author: Segura, Javier
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 16.03.2012; Springer Nature B.V; BioMed Central Ltd
• Subjects: Analysis; Applications of Mathematics; Mathematics; Mathematics and Statistics; zeros of orthogonal polynomials; monotonic difference-differential systems; special function bounds; Riccati equation; three-term recurrence relation; Turán-type inequalities

Many special functions are solutions of first order linear systems y n ′ ( x ) = a n ( x ) y n ( x ) + d n ( x ) y n - 1 ( x ) , y n - 1 ′ ( x ) , = b n ( x ) y n - 1 ( x ) + e n ( x ) y n ( x ) . We obtain bounds for the ratios y n ( x )/ y n -1 ( x ) and the logarithmic derivatives of y n ( x ) fo...