The Mathematical-Function Computation Handbook pp 693-762 | Cite as

# Bessel functions

## Abstract

A large family of functions known as Bessel functions is treated in four chapters of the *Handbook of Mathematical Functions* [AS64, Chapters 9–12], with more coverage than any other named functions in that famous compendium. Although those functions were first discovered by Daniel Bernoulli (1700–1782), who in 1732 worked with the order zero function that is now known as *J* _{ 0 } *(x)*, it was Friedrich Wilhelm Bessel who generalized them about 1824 and brought them to mathematical prominence, and they bear his name, instead of that of Bernoulli. Leonhard Euler (1707–1783) discussed their generalizations to arbitrary integer orders, *J* _{ n } *(x)*, in 1764.

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