Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9735)

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=9/4

http://functions.wolfram.com/07.23.03.9735.01

Input Form

Hypergeometric2F1[-(23/4), 9/4, 11/2, z] == (1/(8021023725 Pi^(3/2) z^(9/2))) (32 (2 (-11306064 + 73085628 z - 163702385 z^2 + 61779564 z^3 + 216228474 z^4 - 787302912 z^5 + 1154897631 z^6 - 967711680 z^7 + 484750848 z^8 - 135954432 z^9 + 16515072 z^10) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-11306064 + 73085628 z - 163702385 z^2 + 61779564 z^3 + 216228474 z^4 - 787302912 z^5 + 1154897631 z^6 - 967711680 z^7 + 484750848 z^8 - 135954432 z^9 + 16515072 z^10) EllipticE[(1/2) (1 + Sqrt[z])] - (-11306064 - 5653032 Sqrt[z] + 73085628 z + 36071728 z^(3/2) - 163702385 z^2 - 79041501 z^(5/2) + 61779564 z^3 + 25438644 z^(7/2) + 216228474 z^4 - 142502646 z^(9/2) - 787302912 z^5 + 236011716 z^(11/2) + 1154897631 z^6 - 212603949 z^(13/2) - 967711680 z^7 + 112257408 z^(15/2) + 484750848 z^8 - 32827392 z^(17/2) - 135954432 z^9 + 4128768 z^(19/2) + 16515072 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (-11306064 + 5653032 Sqrt[z] + 73085628 z - 36071728 z^(3/2) - 163702385 z^2 + 79041501 z^(5/2) + 61779564 z^3 - 25438644 z^(7/2) + 216228474 z^4 + 142502646 z^(9/2) - 787302912 z^5 - 236011716 z^(11/2) + 1154897631 z^6 + 212603949 z^(13/2) - 967711680 z^7 - 112257408 z^(15/2) + 484750848 z^8 + 32827392 z^(17/2) - 135954432 z^9 - 4128768 z^(19/2) + 16515072 z^10) 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]