(For other notation see Notation for the Special Functions.)
|integers. In §§10.47–10.71 is nonnegative.|
|nonnegative integer (except in §10.73).|
|real or complex parameter (the order).|
|arbitrary small positive constant.|
|: logarithmic derivative of the gamma function (§5.2(i)).|
|primes||derivatives with respect to argument, except where indicated otherwise.|
The main functions treated in this chapter are the Bessel functions , ; Hankel functions , ; modified Bessel functions , ; spherical Bessel functions , , , ; modified spherical Bessel functions , , ; Kelvin functions , , , . For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer. For the other functions when the order is replaced by , it can be any integer. For the Kelvin functions the order is always assumed to be real.
A common alternative notation for is . Other notations that have been used are as follows.
Abramowitz and Stegun (1964): , , , , for , , , , respectively, when .
Jeffreys and Jeffreys (1956): for , for , for .
Whittaker and Watson (1927): for .