Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9609)

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=5/4

http://functions.wolfram.com/07.23.03.9609.01

Input Form

Hypergeometric2F1[-(23/4), 5/4, 11/2, z] == (1/(104273308425 Pi^(3/2) z^(9/2))) (32 (2 (56530320 - 530981220 z + 2176047181 z^2 - 4885060873 z^3 + 4133779650 z^4 - 6762562950 z^5 + 6433008465 z^6 - 3991610493 z^7 + 1587990144 z^8 - 369408000 z^9 + 38338560 z^10) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (56530320 - 530981220 z + 2176047181 z^2 - 4885060873 z^3 + 4133779650 z^4 - 6762562950 z^5 + 6433008465 z^6 - 3991610493 z^7 + 1587990144 z^8 - 369408000 z^9 + 38338560 z^10) EllipticE[(1/2) (1 + Sqrt[z])] - (56530320 + 28265160 Sqrt[z] - 530981220 z - 263135180 z^(3/2) + 2176047181 z^2 + 1067077088 z^(5/2) - 4885060873 z^3 - 2362159800 z^(7/2) + 4133779650 z^4 - 1356480840 z^(9/2) - 6762562950 z^5 + 1379438580 z^(11/2) + 6433008465 z^6 - 899346240 z^(13/2) - 3991610493 z^7 + 372483696 z^(15/2) + 1587990144 z^8 - 89656320 z^(17/2) - 369408000 z^9 + 9584640 z^(19/2) + 38338560 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (56530320 - 28265160 Sqrt[z] - 530981220 z + 263135180 z^(3/2) + 2176047181 z^2 - 1067077088 z^(5/2) - 4885060873 z^3 + 2362159800 z^(7/2) + 4133779650 z^4 + 1356480840 z^(9/2) - 6762562950 z^5 - 1379438580 z^(11/2) + 6433008465 z^6 + 899346240 z^(13/2) - 3991610493 z^7 - 372483696 z^(15/2) + 1587990144 z^8 + 89656320 z^(17/2) - 369408000 z^9 - 9584640 z^(19/2) + 38338560 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3991610493 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 899346240 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6433008465 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1379438580 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6762562950 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1356480840 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn 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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]