Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9117)

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=-15/4

http://functions.wolfram.com/07.23.03.9117.01

Input Form

Hypergeometric2F1[-(23/4), -(15/4), 5/2, z] == (1/(2230812675 Pi^(3/2) z^(3/2))) (4 (4 (1110417 - 84391692 z - 2116409477 z^2 - 7544875590 z^3 - 6628154265 z^4 - 1331614096 z^5 - 12711699 z^6 + 306306 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (1110417 - 84391692 z - 2116409477 z^2 - 7544875590 z^3 - 6628154265 z^4 - 1331614096 z^5 - 12711699 z^6 + 306306 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (2220834 + 1110417 Sqrt[z] - 168783384 z - 642002326 z^(3/2) - 4232818954 z^2 - 6863872785 z^(5/2) - 15089751180 z^3 - 16072018740 z^(7/2) - 13256308530 z^4 - 10334202785 z^(9/2) - 2663228192 z^5 - 1522647126 z^(11/2) - 25423398 z^6 + 153153 z^(13/2) + 612612 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (2220834 - 1110417 Sqrt[z] - 168783384 z + 642002326 z^(3/2) - 4232818954 z^2 + 6863872785 z^(5/2) - 15089751180 z^3 + 16072018740 z^(7/2) - 13256308530 z^4 + 10334202785 z^(9/2) - 2663228192 z^5 + 1522647126 z^(11/2) - 25423398 z^6 - 153153 z^(13/2) + 612612 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]