Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6nm)

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=-45/8, b>=a

For fixed z and a=-45/8, b=7/8

http://functions.wolfram.com/07.23.03.b6nm.01

Input Form

Hypergeometric2F1[-(45/8), 7/8, 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-62491520 + 567794045 z - 2413734960 z^2 - 1144344970 z^3 + 1208384140 z^4 - 858665835 z^5 + 390922140 z^6 - 103272960 z^7 + 12063744 z^8) EllipticE[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-62491520 + 567794045 z - 2413734960 z^2 - 1144344970 z^3 + 1208384140 z^4 - 858665835 z^5 + 390922140 z^6 - 103272960 z^7 + 12063744 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-62491520 + 567794045 z - 2413734960 z^2 - 1144344970 z^3 + 1208384140 z^4 - 858665835 z^5 + 390922140 z^6 - 103272960 z^7 + 12063744 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-62491520 + 591228365 z - 2620249905 z^2 + 5130194210 z^3 - 6597819170 z^4 + 6333138945 z^5 - 4142539005 z^6 + 1756497120 z^7 - 436214016 z^8 + 48254976 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (5554386415305 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^3)

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]