Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aa7k)

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=-17/4, b>=a

For fixed z and a=-17/4, b=-17/4

http://functions.wolfram.com/07.23.03.aa7k.01

Input Form

Hypergeometric2F1[-(17/4), -(17/4), 5, -z] == (4096 Sqrt[2] (2 (-42432 - 960024 z - 12591033 z^2 - 163947966 z^3 + 10782826425 z^4 - 32318686428 z^5 + 24147762569 z^6 - 4788145262 z^7 + 169114391 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (-42432 - 960024 z - 12591033 z^2 - 163947966 z^3 + 10782826425 z^4 - 32318686428 z^5 + 24147762569 z^6 - 4788145262 z^7 + 169114391 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-84864 - 1898832 z - 24717303 z^2 - 321932910 z^3 + 12563422275 z^4 - 33310422276 z^5 + 22217681407 z^6 - 3857218142 z^7 + 111035925 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (-42432 - 960024 z - 12591033 z^2 - 163947966 z^3 + 10782826425 z^4 - 32318686428 z^5 + 24147762569 z^6 - 4788145262 z^7 + 169114391 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (18595741539375 Pi z^4 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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<cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 169114391 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4788145262 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 24147762569 </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'> 32318686428 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 10782826425 </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'> 163947966 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> 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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]