Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9u2)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-19/8

http://functions.wolfram.com/07.23.03.b9u2.01

Input Form

Hypergeometric2F1[-(39/8), -(19/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-5770805248 + 103175686016 z - 957514626445 z^2 + 6685771280734 z^3 - 50458291181207 z^4 - 853552134385832 z^5 - 1056510864676491 z^6 - 239990789917050 z^7 - 584185798449 z^8 + 18496647972 z^9) 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) (-5770805248 + 103175686016 z - 957514626445 z^2 + 6685771280734 z^3 - 50458291181207 z^4 - 853552134385832 z^5 - 1056510864676491 z^6 - 239990789917050 z^7 - 584185798449 z^8 + 18496647972 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-5770805248 + 103175686016 z - 957514626445 z^2 + 6685771280734 z^3 - 50458291181207 z^4 - 853552134385832 z^5 - 1056510864676491 z^6 - 239990789917050 z^7 - 584185798449 z^8 + 18496647972 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-5770805248 + 105339737984 z - 995613775741 z^2 + 7034574085669 z^3 - 52872687401261 z^4 + 832145238170365 z^5 + 2355730849035921 z^6 + 1170073322197671 z^7 + 81587172817161 z^8 - 2372195102409 z^9 + 73986591888 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(437102165472901343415 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]