Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab10)

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=-15/4, b>=a

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

http://functions.wolfram.com/07.23.03.ab10.01

Input Form

Hypergeometric2F1[-(15/4), -(15/4), 3, -z] == (64 Sqrt[2] (-2 Sqrt[1 + z] (770 + 25025 z - 1039328 z^2 + 2773022 z^3 - 1423402 z^4 + 114713 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 2 (770 + 25795 z - 1014303 z^2 + 1733694 z^3 + 1349620 z^4 - 1308689 z^5 + 114713 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (770 + 25025 z - 1039328 z^2 + 2773022 z^3 - 1423402 z^4 + 114713 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (1540 + 51205 z + 256369 z^2 - 6642798 z^3 + 10921222 z^4 - 3559911 z^5 + 168245 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (73523065 Pi z^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> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </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]