Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9723)

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/07.23.03.9723.01

Input Form

Hypergeometric2F1[-(23/4), 9/4, 5/2, z] == (1/(16823625 Pi^(3/2) z^(3/2))) (4 (4 (100947 + 1110417 z - 10811899 z^2 + 32050935 z^3 - 47109600 z^4 + 37762304 z^5 - 15876096 z^6 + 2752512 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (100947 + 1110417 z - 10811899 z^2 + 32050935 z^3 - 47109600 z^4 + 37762304 z^5 - 15876096 z^6 + 2752512 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (201894 + 100947 Sqrt[z] + 2220834 z - 3087077 z^(3/2) - 21623798 z^2 + 11576145 z^(5/2) + 64101870 z^3 - 19314495 z^(7/2) - 94219200 z^4 + 16858240 z^(9/2) + 75524608 z^5 - 7550976 z^(11/2) - 31752192 z^6 + 1376256 z^(13/2) + 5505024 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (201894 - 100947 Sqrt[z] + 2220834 z + 3087077 z^(3/2) - 21623798 z^2 - 11576145 z^(5/2) + 64101870 z^3 + 19314495 z^(7/2) - 94219200 z^4 - 16858240 z^(9/2) + 75524608 z^5 + 7550976 z^(11/2) - 31752192 z^6 - 1376256 z^(13/2) + 5505024 z^7) 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]