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

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=-7/8

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

Input Form

Hypergeometric2F1[-(35/8), -(7/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-431456256 + 5799378816 z - 38568183885 z^2 + 180473683005 z^3 - 826748424810 z^4 - 5944116657894 z^5 - 1721690324081 z^6 + 146513275545 z^7 - 15735425160 z^8 + 975840320 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-431456256 + 5961174912 z - 40698709821 z^2 + 194365592190 z^3 - 890771843115 z^4 + 8576019986196 z^5 + 8549003294173 z^6 + 37344189246 z^7 - 3979598805 z^8 + 243960080 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) (-431456256 + 5799378816 z - 38568183885 z^2 + 180473683005 z^3 - 826748424810 z^4 - 5944116657894 z^5 - 1721690324081 z^6 + 146513275545 z^7 - 15735425160 z^8 + 975840320 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-431456256 + 5799378816 z - 38568183885 z^2 + 180473683005 z^3 - 826748424810 z^4 - 5944116657894 z^5 - 1721690324081 z^6 + 146513275545 z^7 - 15735425160 z^8 + 975840320 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (3729445672348571175 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]