Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9173)

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=-13/4

http://functions.wolfram.com/07.23.03.9173.01

Input Form

Hypergeometric2F1[-(23/4), -(13/4), 4, -z] == (1/(5446254688875 Pi z^3)) (256 (1 + z)^(1/4) (2 (-1999712 - 54304679 z - 1102341240 z^2 + 70816221315 z^3 - 250544241150 z^4 + 206576582751 z^5 - 37907014908 z^6 + 42879525 z^7 + 1292850 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (-1999712 - 54304679 z - 1102341240 z^2 + 70816221315 z^3 - 250544241150 z^4 + 206576582751 z^5 - 37907014908 z^6 + 42879525 z^7 + 1292850 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (1999712 + 52804895 z + 1062971910 z^2 - 29058485295 z^3 + 71018115000 z^4 - 37628288271 z^5 + 3098099550 z^6 + 83819775 z^7 + 2585700 z^8) EllipticK[1/2 - 1/(2 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]