Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9og)

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=-35/8

http://functions.wolfram.com/07.23.03.b9og.01

Input Form

Hypergeometric2F1[-(39/8), -(35/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (17312415744 - 395007110784 z + 4835913840615 z^2 - 46500576503745 z^3 + 511678387899315 z^4 + 15270793787238331 z^5 + 37874838495883669 z^6 + 25493998769706045 z^7 + 4912415543096465 z^8 + 192369660407945 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) (17312415744 - 395007110784 z + 4835913840615 z^2 - 46500576503745 z^3 + 511678387899315 z^4 + 15270793787238331 z^5 + 37874838495883669 z^6 + 25493998769706045 z^7 + 4912415543096465 z^8 + 192369660407945 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (17312415744 - 395007110784 z + 4835913840615 z^2 - 46500576503745 z^3 + 511678387899315 z^4 + 15270793787238331 z^5 + 37874838495883669 z^6 + 25493998769706045 z^7 + 4912415543096465 z^8 + 192369660407945 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-17312415744 + 401499266688 z - 4982266308279 z^2 + 48274483609560 z^3 - 528641134372260 z^4 + 11515765654238504 z^5 + 60375581251689302 z^6 + 70452766588230504 z^7 + 24357306961969180 z^8 + 2188412433824920 z^9 + 23236414014825 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(6972820258734378573525 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]