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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 21BESSEL FUNCTIONS

‘Mine is a long and a sad tale!’ said the Mouse, turning to Alice, and sighing.‘It is a long tail, certainly’, said Alice, looking down with wonder at the Mouse’s tail; ‘but why do you call it sad?’

LEWIS CARROLL, Alice’s Adventures in Wonderland

21·01. Definitions of J±n(x), I±n(x).

We have already had (16·10,18·03) the functions

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The corresponding series with all the signs taken positive are

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Clearly

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The differential ...

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