# Herglotz generating function

(0.001 seconds)

## 11—20 of 949 matching pages

##### 11: 15.2 Definitions and Analytical Properties
###### §15.2(i) Gauss Series
The hypergeometric function $F\left(a,b;c;z\right)$ is defined by the Gauss series … … On the circle of convergence, $|z|=1$, the Gauss series: …
##### 12: 5.12 Beta Function
###### Euler’s Beta Integral Figure 5.12.1: t -plane. Contour for first loop integral for the beta function. Magnify Figure 5.12.2: t -plane. Contour for second loop integral for the beta function. Magnify
##### 14: 10.1 Special Notation
(For other notation see Notation for the Special Functions.) … For the spherical Bessel functions and modified spherical Bessel functions the order $n$ is a nonnegative integer. For the other functions when the order $\nu$ is replaced by $n$, it can be any integer. For the Kelvin functions the order $\nu$ is always assumed to be real. … For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
##### 16: 25.1 Special Notation
(For other notation see Notation for the Special Functions.)
 $k,m,n$ nonnegative integers. … on function symbols: derivatives with respect to argument.
The main function treated in this chapter is the Riemann zeta function $\zeta\left(s\right)$. … The main related functions are the Hurwitz zeta function $\zeta\left(s,a\right)$, the dilogarithm $\mathrm{Li}_{2}\left(z\right)$, the polylogarithm $\mathrm{Li}_{s}\left(z\right)$ (also known as Jonquière’s function $\phi\left(z,s\right)$), Lerch’s transcendent $\Phi\left(z,s,a\right)$, and the Dirichlet $L$-functions $L\left(s,\chi\right)$.
##### 17: 12.1 Special Notation
(For other notation see Notation for the Special Functions.) … Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values. The main functions treated in this chapter are the parabolic cylinder functions (PCFs), also known as Weber parabolic cylinder functions: $U\left(a,z\right)$, $V\left(a,z\right)$, $\overline{U}\left(a,z\right)$, and $W\left(a,z\right)$. …An older notation, due to Whittaker (1902), for $U\left(a,z\right)$ is $D_{\nu}\left(z\right)$. …
##### 18: 17.1 Special Notation
###### §17.1 Special Notation
(For other notation see Notation for the Special Functions.)
 $k,j,m,n,r,s$ nonnegative integers. …
Another function notation used is the “idem” function: …
##### 19: 4.37 Inverse Hyperbolic Functions
###### §4.37(i) General Definitions
Each of the six functions is a multivalued function of $z$. …