Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6ay)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-25/8

http://functions.wolfram.com/07.23.03.b6ay.01

Input Form

Hypergeometric2F1[-(45/8), -(25/8), 2, z] == (16 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-41498275 - 13550468793 z - 99541252010 z^2 - 139583291570 z^3 - 38867000615 z^4 - 23445125 z^5 + 953700 z^6) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-41498275 - 13550468793 z - 99541252010 z^2 - 139583291570 z^3 - 38867000615 z^4 - 23445125 z^5 + 953700 z^6) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-41498275 - 13550468793 z - 99541252010 z^2 - 139583291570 z^3 - 38867000615 z^4 - 23445125 z^5 + 953700 z^6) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-41498275 - 4462346568 z - 17693204747 z^2 + 2644647400 z^3 + 17158217815 z^4 + 2485978000 z^5 - 95608425 z^6 + 3814800 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (72580482975 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z)

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]