Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9074)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=-17/4

http://functions.wolfram.com/07.23.03.9074.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 1, z] == (1/(334639305 Pi)) (2 Sqrt[1 + Sqrt[z]] ((728420683 + 12959599657 z + 38890777198 z^2 + 27874724562 z^3 + 4101448695 z^4 + 2197845 z^5) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 2 (-196890689 + 196890689 Sqrt[z] - 2528136359 z + 2528136359 z^(3/2) - 5325406682 z^2 + 5325406682 z^(5/2) - 2378550270 z^3 + 2378550270 z^(7/2) - 142859925 z^4 + 142859925 z^(9/2) + 2197845 z^5 - 2197845 z^(11/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]