Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bar1)

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=43/8

http://functions.wolfram.com/07.23.03.bar1.01

Input Form

Hypergeometric2F1[-(39/8), 43/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (-303726592 - 447284864 z - 852182591 z^2 - 2318658888 z^3 - 11745445075 z^4 + 234772384490 z^5 - 674337975920 z^6 + 815166349920 z^7 - 459946755840 z^8 + 100164979200 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-303726592 - 447284864 z - 852182591 z^2 - 2318658888 z^3 - 11745445075 z^4 + 234772384490 z^5 - 674337975920 z^6 + 815166349920 z^7 - 459946755840 z^8 + 100164979200 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-303726592 - 447284864 z - 852182591 z^2 - 2318658888 z^3 - 11745445075 z^4 + 234772384490 z^5 - 674337975920 z^6 + 815166349920 z^7 - 459946755840 z^8 + 100164979200 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-303726592 - 257455744 z - 541485711 z^2 - 1725581923 z^3 - 10178520625 z^4 - 182860346025 z^5 + 1057458801980 z^6 - 2144187101680 z^7 + 2111733711360 z^8 - 1030074988800 z^9 + 200329958400 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (111482385870340485 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]