On the Order Derivatives of Bessel Functions

被引：9

作者：

Dunster, T. M. ^{[1
]}

机构：

[1] San Diego State Univ, Dept Math & Stat, San Diego, CA 92182 USA

来源：

CONSTRUCTIVE APPROXIMATION | 2017年 / 46卷 / 01期

关键词：

Bessel functions; Asymptotic approximations; Series expansions; RESPECT; INTEGRALS;

D O I：

10.1007/s00365-016-9355-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The derivatives with respect to order for the Bessel functions and , where and (real or complex), are studied. Representations are derived in terms of integrals that involve the products pairs of Bessel functions, and in turn series expansions are obtained for these integrals. From the new integral representations for and , asymptotic approximations involving Airy functions are constructed for the case large, which are uniformly valid for 0 < x < infinity.

引用

页码：47 / 68

页数：22

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