Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abf0)

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=5/4

http://functions.wolfram.com/07.23.03.abf0.01

Input Form

Hypergeometric2F1[-(15/4), 5/4, 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (1760 + 9405 z + 17325 z^2 + 32947 z^3 + 27747 z^4 + 11808 z^5 + 2048 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (1760 + 11165 z + 26730 z^2 + 50272 z^3 + 60694 z^4 + 39555 z^5 + 13856 z^6 + 2048 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (1760 + 10725 z + 24255 z^2 + 9847 z^3 + 7701 z^4 + 3096 z^5 + 512 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (1760 + 9405 z + 17325 z^2 + 32947 z^3 + 27747 z^4 + 11808 z^5 + 2048 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4542615 Pi z^3 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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type='integer'> -1 </cn> </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]