Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9847)

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=13/4

http://functions.wolfram.com/07.23.03.9847.01

Input Form

Hypergeometric2F1[-(23/4), 13/4, 3/2, z] == (1/(745875 Pi^(3/2) Sqrt[z])) (2 (2 (100947 - 3270966 z + 20091875 z^2 - 50119040 z^3 + 60917760 z^4 - 36110336 z^5 + 8388608 z^6) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (100947 - 3270966 z + 20091875 z^2 - 50119040 z^3 + 60917760 z^4 - 36110336 z^5 + 8388608 z^6) EllipticE[(1/2) (1 + Sqrt[z])] - (100947 - 322464 Sqrt[z] - 3270966 z + 3061520 z^(3/2) + 20091875 z^2 - 9409520 z^(5/2) - 50119040 z^3 + 13009920 z^(7/2) + 60917760 z^4 - 8437760 z^(9/2) - 36110336 z^5 + 2097152 z^(11/2) + 8388608 z^6) EllipticK[(1/2) (1 - Sqrt[z])] + (100947 + 322464 Sqrt[z] - 3270966 z - 3061520 z^(3/2) + 20091875 z^2 + 9409520 z^(5/2) - 50119040 z^3 - 13009920 z^(7/2) + 60917760 z^4 + 8437760 z^(9/2) - 36110336 z^5 - 2097152 z^(11/2) + 8388608 z^6) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 60917760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13009920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 50119040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9409520 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20091875 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3061520 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3270966 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 322464 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 100947 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]