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

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=-35/8, b>=a

For fixed z and a=-35/8, b=17/8

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

Input Form

Hypergeometric2F1[-(35/8), 17/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (20545536 - 131700096 z + 321246585 z^2 - 296784180 z^3 - 148392090 z^4 + 962036364 z^5 - 1221249239 z^6 + 779832480 z^7 - 260279040 z^8 + 36270080 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (20545536 - 139404672 z + 368527401 z^2 - 404866440 z^3 - 63596610 z^4 + 283672524 z^5 - 336579263 z^6 + 206351124 z^7 - 66769920 z^8 + 9067520 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (20545536 - 131700096 z + 321246585 z^2 - 296784180 z^3 - 148392090 z^4 + 962036364 z^5 - 1221249239 z^6 + 779832480 z^7 - 260279040 z^8 + 36270080 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (20545536 - 131700096 z + 321246585 z^2 - 296784180 z^3 - 148392090 z^4 + 962036364 z^5 - 1221249239 z^6 + 779832480 z^7 - 260279040 z^8 + 36270080 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (196898034546675 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]