Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9732)

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=9/4

http://functions.wolfram.com/07.23.03.9732.01

Input Form

Hypergeometric2F1[-(23/4), 9/4, 5, z] == (1/(64073584575 Pi z^4)) (4096 (-16 Sqrt[1 - z] (76912 - 394174 z + 504735 z^2 + 706629 z^3 - 5074447 z^4 + 9516129 z^5 - 9456888 z^6 + 5428160 z^7 - 1708032 z^8 + 229376 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + 8 Sqrt[1 - z] (76912 - 394174 z + 504735 z^2 + 706629 z^3 - 5074447 z^4 + 9516129 z^5 - 9456888 z^6 + 5428160 z^7 - 1708032 z^8 + 229376 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (615296 - 3614864 z + 6359661 z^2 + 2826516 z^3 - 13743674 z^4 + 23193492 z^5 - 21562443 z^6 + 11757952 z^7 - 3545088 z^8 + 458752 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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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]