Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9031)

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=-19/4

http://functions.wolfram.com/07.23.03.9031.01

Input Form

Hypergeometric2F1[-(23/4), -(19/4), 2, -z] == (1/(4542615 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] ((-Sqrt[1 + z]) (7315 - 1328598 z + 11422845 z^2 - 22006324 z^3 + 11422845 z^4 - 1328598 z^5 + 7315 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (7315 - 1321283 z + 10094247 z^2 - 10583479 z^3 - 10583479 z^4 + 10094247 z^5 - 1321283 z^6 + 7315 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (7315 - 1328598 z + 11422845 z^2 - 22006324 z^3 + 11422845 z^4 - 1328598 z^5 + 7315 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-7315 + 187458 z + 5011911 z^2 - 31703540 z^3 + 42287019 z^4 - 15106158 z^5 + 1133825 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (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]