Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bknp)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-23/8, b>=a

For fixed z and a=-23/8, b=43/8

http://functions.wolfram.com/07.23.03.bknp.01

Input Form

Hypergeometric2F1[-(23/8), 43/8, 5, z] == (65536 2^(1/4) (8 Sqrt[1 - z] (-17664 - 65320 z - 231955 z^2 - 1200370 z^3 + 18630300 z^4 - 32513520 z^5 + 15381600 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-17664 - 65320 z - 231955 z^2 - 1200370 z^3 + 18630300 z^4 - 32513520 z^5 + 15381600 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 Sqrt[1 - z] (-17664 - 65320 z - 231955 z^2 - 1200370 z^3 + 18630300 z^4 - 32513520 z^5 + 15381600 z^6) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-70656 - 217120 z - 757275 z^2 - 4191405 z^3 - 66786200 z^4 + 277027920 z^5 - 327787200 z^6 + 123052800 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (4732291889325 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]