Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8z6)

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=23/4

http://functions.wolfram.com/07.23.03.a8z6.01

Input Form

Hypergeometric2F1[-(21/4), 23/4, 6, z] == (1/(35204273129025 Pi z^5)) (16384 (-2 (1357824 + 2694432 z + 7236645 z^2 + 27143883 z^3 + 182826891 z^4 - 6906897691 z^5 + 28390727712 z^6 - 50384701440 z^7 + 46067089408 z^8 - 21416116224 z^9 + 4026531840 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-1357824 - 3033888 z - 8154237 z^2 - 29637426 z^3 - 191484345 z^4 + 2557349176 z^5 - 6961069568 z^6 + 8262320128 z^7 - 4630511616 z^8 + 1006632960 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (1357824 + 2694432 z + 7236645 z^2 + 27143883 z^3 + 182826891 z^4 - 6906897691 z^5 + 28390727712 z^6 - 50384701440 z^7 + 46067089408 z^8 - 21416116224 z^9 + 4026531840 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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</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]