Bessel function

Modified Bessel functions of 1st kind, Iα(x), for α = 0, 1, 2, 3

Modified Bessel functions of 2nd kind, Kα(x), for α = 0, 1, 2, 3

Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions y(x) of the differential equation

(known as Bessel's differential equation) for an arbitrary complex number $α$ , the order of the Bessel function. Although $α$ and − $α$ produce the same differential equation for real $α$ , it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of $α$ .

单词	Modified Hankel functions
释义	Modified Hankel functions 英语百科 Bessel function Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions y(x) of the differential equation (known as Bessel's differential equation) for an arbitrary complex number $α$ , the order of the Bessel function. Although $α$ and − $α$ produce the same differential equation for real $α$ , it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of $α$ .
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Modified Hankel functions

Bessel function