Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9671)

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=7/4

http://functions.wolfram.com/07.23.03.9671.01

Input Form

Hypergeometric2F1[-(23/4), 7/4, 6, -z] == (1/(9210120114195 Pi z^5)) (16384 (1 + z)^(1/4) (2 (9844736 + 84141728 z + 299279013 z^2 + 522285357 z^3 + 196846650 z^4 + 542313018 z^5 + 639270489 z^6 + 451434009 z^7 + 196495416 z^8 + 48906000 z^9 + 5353920 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (9844736 + 84141728 z + 299279013 z^2 + 522285357 z^3 + 196846650 z^4 + 542313018 z^5 + 639270489 z^6 + 451434009 z^7 + 196495416 z^8 + 48906000 z^9 + 5353920 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-9844736 - 76758176 z - 242864061 z^2 - 348699780 z^3 + 39369330 z^4 + 520658892 z^5 + 800909187 z^6 + 664256112 z^7 + 326458080 z^8 + 89781120 z^9 + 10707840 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </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]