Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bj5y)

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=-25/8, b>=a

For fixed z and a=-25/8, b=19/8

http://functions.wolfram.com/07.23.03.bj5y.01

Input Form

Hypergeometric2F1[-(25/8), 19/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-8355840 + 43900800 z - 82792125 z^2 + 49542675 z^3 + 28426125 z^4 - 319877103 z^5 + 353438540 z^6 - 164702720 z^7 + 29352960 z^8) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-8355840 + 47034240 z - 98398125 z^2 + 76543350 z^3 + 16243500 z^4 - 93280278 z^5 + 95426513 z^6 - 42551600 z^7 + 7338240 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-8355840 + 43900800 z - 82792125 z^2 + 49542675 z^3 + 28426125 z^4 - 319877103 z^5 + 353438540 z^6 - 164702720 z^7 + 29352960 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-8355840 + 43900800 z - 82792125 z^2 + 49542675 z^3 + 28426125 z^4 - 319877103 z^5 + 353438540 z^6 - 164702720 z^7 + 29352960 z^8) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (62698383923175 Pi (1 + Sqrt[1 - z])^(1/4) (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]