§11.1 Special Notation

Keywords:: Anger–Weber functions, Lommel functions, Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.1

(For other notation see Notation for the Special Functions.)

$x$	real variable.
$z$	complex variable.
$\nu$	real or complex order.
$n$	integer order.
$k$	nonnegative integer.
$\delta$	arbitrary small positive constant.

Unless indicated otherwise, primes denote derivatives with respect to the argument. For the functions $\mathop{J_{{\nu}}\/}\nolimits\!\left(z\right)$ , $\mathop{Y_{{\nu}}\/}\nolimits\!\left(z\right)$ , $\mathop{{H^{{(1)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$ , $\mathop{{H^{{(2)}}_{{\nu}}}\/}\nolimits\!\left(z\right)$ , $\mathop{I_{{\nu}}\/}\nolimits\!\left(z\right)$ , and $\mathop{K_{{\nu}}\/}\nolimits\!\left(z\right)$ see §§10.2(ii), 10.25(ii).

The functions treated in this chapter are the Struve functions $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ and $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ , the modified Struve functions $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(z\right)$ and $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(z\right)$ , the Lommel functions $\mathop{s_{{{\mu},{\nu}}}\/}\nolimits\!\left(z\right)$ and $\mathop{S_{{{\mu},{\nu}}}\/}\nolimits\!\left(z\right)$ , the Anger function $\mathop{\mathbf{J}_{{\nu}}\/}\nolimits\!\left(z\right)$ , the Weber function $\mathop{\mathbf{E}_{{\nu}}\/}\nolimits\!\left(z\right)$ , and the associated Anger–Weber function $\mathop{\mathbf{A}_{{\nu}}\/}\nolimits\!\left(z\right)$ .