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

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=-17/4, b>=a

For fixed z and a=-17/4, b=19/4

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

Input Form

Hypergeometric2F1[-(17/4), 19/4, 6, -z] == (16384 Sqrt[2] ((-1357824 - 700128 z + 825435 z^2 - 1762917 z^3 + 7480629 z^4 + 174394869 z^5 + 472523648 z^6 + 536033280 z^7 + 284884992 z^8 + 58720256 z^9) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (-1357824 - 700128 z + 825435 z^2 - 1762917 z^3 + 7480629 z^4 + 174394869 z^5 + 472523648 z^6 + 536033280 z^7 + 284884992 z^8 + 58720256 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-1357824 - 360672 z + 756483 z^2 - 1894854 z^3 + 7999095 z^4 + 56304624 z^5 + 91476992 z^6 + 60669952 z^7 + 14680064 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-1357824 - 700128 z + 825435 z^2 - 1762917 z^3 + 7480629 z^4 + 174394869 z^5 + 472523648 z^6 + 536033280 z^7 + 284884992 z^8 + 58720256 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (949024050975 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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</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]