Table of Integrals, Series, and Products, 8th Edition

Index of Special Functions

Notation	Name of the function and the number of the formula containing its definition
β(x)	8.37
Γ(z)	Gamma function	8.31–8.33
γ(a,x), Γ(a, x)	Incomplete gamma functions	8.35
Δ(n — k)	Unit integer pulse function	18.1
ξ(s)	9.56
λ(x,y)	9.640
μ(x,β), μ(x,β,α)	9.640
ν(x),ν(x,α)	9.640
П(x)	Lobachevskiy angle of parallelism	1.48
П(φ, n,k)	Elliptic integral of the third kind	8.11
ζ (u)	Weierstrass zeta function	8.17
ζ(z,q), ζ(z)	Riemann zeta functions	9.51-9.54
$\Theta (u)={\vartheta }_4(\frac{\pi u}{2K}),{\Theta }_1(u)={\vartheta }_3(\frac{\pi u}{2K})$	Jacobi theta function	8.191-8.196
$\left\{\begin{array}{l}{\vartheta }_0(\nu |\tau )={\vartheta }_4(\nu |\tau ),\hfill \\ {\vartheta }_1(\nu |\tau ),{\vartheta }_2(\nu |\tau ),\hfill \\ {\vartheta }_3(\nu |\tau )\hfill \end{array}\right\}$	Elliptic theta functions	8.18, 8.19
σ(u)	Weierstrass sigma function	8.17
ϕ(x)	Probability integral ...