Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b50c)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-3/8

http://functions.wolfram.com/07.23.03.b50c.01

Input Form

Hypergeometric2F1[-(47/8), -(3/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (14275149824 - 203922745728 z + 1436647366609 z^2 - 7047610276070 z^3 + 32887633237095 z^4 + 211703371515356 z^5 + 9732879560943 z^6 - 2626608939174 z^7 + 591936978105 z^8 - 89275420080 z^9 + 6522405120 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (14275149824 - 203922745728 z + 1436647366609 z^2 - 7047610276070 z^3 + 32887633237095 z^4 + 211703371515356 z^5 + 9732879560943 z^6 - 2626608939174 z^7 + 591936978105 z^8 - 89275420080 z^9 + 6522405120 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (14275149824 - 203922745728 z + 1436647366609 z^2 - 7047610276070 z^3 + 32887633237095 z^4 + 211703371515356 z^5 + 9732879560943 z^6 - 2626608939174 z^7 + 591936978105 z^8 - 89275420080 z^9 + 6522405120 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (14275149824 - 209275926912 z + 1511654635777 z^2 - 7566220614134 z^3 + 35393774148915 z^4 - 330291821007064 z^5 - 225984246102153 z^6 + 43731969750018 z^7 - 11604379209291 z^8 + 2536084847340 z^9 - 369602956800 z^10 + 26089620480 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (139018535180314584795 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

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]