Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9199)

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=-11/4

http://functions.wolfram.com/07.23.03.9199.01

Input Form

Hypergeometric2F1[-(23/4), -(11/4), 3/2, z] == (1/(9696375 Pi^(3/2) Sqrt[z])) (2 (-2 (1110417 + 42825399 z + 156871450 z^2 + 98382110 z^3 + 3030885 z^4 - 244101 z^5 + 13728 z^6) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (1110417 + 42825399 z + 156871450 z^2 + 98382110 z^3 + 3030885 z^4 - 244101 z^5 + 13728 z^6) EllipticE[(1/2) (1 + Sqrt[z])] + (1110417 + 5403396 Sqrt[z] + 42825399 z + 71960920 z^(3/2) + 156871450 z^2 + 158581880 z^(5/2) + 98382110 z^3 + 66100320 z^(7/2) + 3030885 z^4 - 60060 z^(9/2) - 244101 z^5 + 3432 z^(11/2) + 13728 z^6) EllipticK[(1/2) (1 - Sqrt[z])] - (1110417 - 5403396 Sqrt[z] + 42825399 z - 71960920 z^(3/2) + 156871450 z^2 - 158581880 z^(5/2) + 98382110 z^3 - 66100320 z^(7/2) + 3030885 z^4 + 60060 z^(9/2) - 244101 z^5 - 3432 z^(11/2) + 13728 z^6) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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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]