Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9gj)

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=-19/4, b>=a

For fixed z and a=-19/4, b=5/4

http://functions.wolfram.com/07.23.03.a9gj.01

Input Form

Hypergeometric2F1[-(19/4), 5/4, 9/2, z] == (1/(47586825 Pi^(3/2) z^(7/2))) (16 (-8 (43890 - 320397 z + 946561 z^2 - 921690 z^3 + 1570140 z^4 - 1431705 z^5 + 776241 z^6 - 235008 z^7 + 30720 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 8 (43890 - 320397 z + 946561 z^2 - 921690 z^3 + 1570140 z^4 - 1431705 z^5 + 776241 z^6 - 235008 z^7 + 30720 z^8) EllipticE[(1/2) (1 + Sqrt[z])] + (175560 + 87780 Sqrt[z] - 1281588 z - 633479 z^(3/2) + 3786244 z^2 + 1843380 z^(5/2) - 3686760 z^3 + 1264230 z^(7/2) + 6280560 z^4 - 1246080 z^(9/2) - 5726820 z^5 + 714825 z^(11/2) + 3104964 z^6 - 226368 z^(13/2) - 940032 z^7 + 30720 z^(15/2) + 122880 z^8) EllipticK[(1/2) (1 - Sqrt[z])] - (175560 - 87780 Sqrt[z] - 1281588 z + 633479 z^(3/2) + 3786244 z^2 - 1843380 z^(5/2) - 3686760 z^3 - 1264230 z^(7/2) + 6280560 z^4 + 1246080 z^(9/2) - 5726820 z^5 - 714825 z^(11/2) + 3104964 z^6 + 226368 z^(13/2) - 940032 z^7 - 30720 z^(15/2) + 122880 z^8) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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<cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1570140 </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'> 921690 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 946561 </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'> 320397 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 43890 </cn> </apply> <apply> <ci> EllipticE </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> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 122880 </cn> 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type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1246080 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6280560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1264230 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3686760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1843380 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3786244 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 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]