Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7v7)

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=23/4

http://functions.wolfram.com/07.23.03.a7v7.01

Input Form

Hypergeometric2F1[-(23/4), 23/4, 6, -z] == (1/(1653098482035 Pi z^5)) (16384 (1 + z)^(1/4) (2 (47104 - 103776 z + 292629 z^2 - 1146481 z^3 + 8107155 z^4 + 168992733 z^5 + 616225428 z^6 + 1017242928 z^7 + 881906688 z^8 + 392920320 z^9 + 71285760 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (47104 - 103776 z + 292629 z^2 - 1146481 z^3 + 8107155 z^4 + 168992733 z^5 + 616225428 z^6 + 1017242928 z^7 + 881906688 z^8 + 392920320 z^9 + 71285760 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-47104 + 139104 z - 402477 z^2 + 1466710 z^3 - 9261525 z^4 + 39940992 z^5 + 452015928 z^6 + 1129729536 z^7 + 1265322240 z^8 + 678912000 z^9 + 142571520 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

Standard Form

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MathML Form

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<cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]