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

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=-17/8, b>=a

For fixed z and a=-17/8, b=5/8

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

Input Form

Hypergeometric2F1[-(17/8), 5/8, 5, z] == (1/(52999479225 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-17408 + 119136 z - 359703 z^2 + 674985 z^3 + 1497903 z^4 - 390621 z^5 + 52668 z^6) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-2176 + 14535 z - 42687 z^2 + 401523 z^3 - 64581 z^4 + 8778 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (2176 - 13311 z + 35445 z^2 + 479655 z^3 - 127281 z^4 + 17556 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-17408 + 119136 z - 359703 z^2 + 674985 z^3 + 1497903 z^4 - 390621 z^5 + 52668 z^6) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]