Selected Special Functions for Fundamental Physics by Valeriya Akhmedova & Emil T. Akhmedov

Author:Valeriya Akhmedova & Emil T. Akhmedov
Language: eng
Format: epub
ISBN: 9783030350895
Publisher: Springer International Publishing

Thus, , can be used as a basis of such functions on the interval that vanish at .

5.12 Addition or Summation Theorems for

Bessel functions obey an important relation, which we will derive in this subsection. Consider the following sequence of equalities:

where we have used the expression for the generating function.

Thus,

Equating the expressions which multiply equal powers of on both sides of this relation for each n separately, we obtain:

which is the so called summation relation for the Bessel functions. It is similar in spirit to the relation between the trigonometric functions, which follow from the simple relation .

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