Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8hq)

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=-21/4, b>=a

For fixed z and a=-21/4, b=1/4

http://functions.wolfram.com/07.23.03.a8hq.01

Input Form

Hypergeometric2F1[-(21/4), 1/4, 5, -z] == (1/(225958107375 Pi z^4)) (4096 (1 + z)^(1/4) (4 (-42432 - 482664 z - 2695095 z^2 - 11294205 z^3 + 55665170 z^4 + 21060006 z^5 + 9076837 z^6 + 2925615 z^7 + 591360 z^8 + 55440 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-84864 - 901680 z - 4723875 z^2 - 19147440 z^3 + 14843950 z^4 + 6865452 z^5 + 2432045 z^6 + 540540 z^7 + 55440 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - 2 (-42432 - 482664 z - 2695095 z^2 - 11294205 z^3 + 55665170 z^4 + 21060006 z^5 + 9076837 z^6 + 2925615 z^7 + 591360 z^8 + 55440 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 482664 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -42432 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 55440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 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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]