Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9929)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=15/4

http://functions.wolfram.com/07.23.03.9929.01

Input Form

Hypergeometric2F1[-(23/4), 15/4, 6, -z] == (1/(551032827345 Pi z^5)) (16384 (1 + z)^(1/4) (2 (894976 + 2838752 z + 749455 z^2 - 1319740 z^3 + 4741450 z^4 + 47894028 z^5 + 112510671 z^6 + 130969800 z^7 + 84673680 z^8 + 29265600 z^9 + 4243200 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (894976 + 2838752 z + 749455 z^2 - 1319740 z^3 + 4741450 z^4 + 47894028 z^5 + 112510671 z^6 + 130969800 z^7 + 84673680 z^8 + 29265600 z^9 + 4243200 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-894976 - 2167520 z + 771305 z^2 + 526585 z^3 - 4970875 z^4 + 23090067 z^5 + 107133390 z^6 + 167310000 z^7 + 130859040 z^8 + 52166400 z^9 + 8486400 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

Standard Form

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MathML Form

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</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]