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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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Index of Special Functions

NotationName of the function and the number of the formula containing its definition
β(x)8.37
Γ(z)Gamma function8.31–8.33
γ(a,x), Γ(a, x)Incomplete gamma functions8.35
Δ(nk)Unit integer pulse function18.1
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 parallelism1.48
П(φ, n,k)Elliptic integral of the third kind8.11
ζ (u)Weierstrass zeta function8.17
ζ(z,q), ζ(z)Riemann zeta functions9.51-9.54
Θ(u)=ϑ4(πu2K),  Θ1(u)=ϑ3(πu2K)si1_eJacobi theta function8.191-8.196
{ϑ0(ν|τ)=ϑ4(ν|τ),ϑ1(ν|τ),  ϑ2(ν|τ),ϑ3(ν|τ)}Elliptic theta functions8.18, 8.19
σ(u)Weierstrass sigma function8.17
ϕ(x)Probability integral ...

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