“Bessel Differential Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Bessel Differential Equation

释义

Bessel Differential Equation

(1)

Equivalently, dividing through by

(2)

The solutions to this equation define the Bessel Functions. The equation has a regularSingularity at 0 and an irregular Singularity at

A transformed version of the Bessel differential equation given by Bowman (1958) is

(3)

The solution is

(4)

where

(5)

and

are the Bessel Functions of the First andSecond Kinds, and

and

are constants. Another formis given by letting

, and

(Bowman 1958, p. 117),then

(6)

The solution is

(7)

See also Airy Functions, Anger Function, Bei, Ber,Bessel Function, Bourget's Hypothesis, Catalan Integrals, Cylindrical Function, DiniExpansion, Hankel Function, Hankel's Integral, Hemispherical Function, Kapteyn Series,Lipschitz's Integral, Lommel Differential Equation, Lommel Function, Lommel's Integrals,Neumann Series (Bessel Function), Parseval's Integral, Poisson Integral, Ramanujan's Integral,Riccati Differential Equation, Sonine's Integral, Struve Function, Weber Functions,Weber's Discontinuous Integrals

References

Bowman, F. Introduction to Bessel Functions. New York: Dover, 1958.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 550, 1953.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。