Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4y6)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-47/8, b>=a

For fixed z and a=-47/8, b=-9/8

http://functions.wolfram.com/07.23.03.b4y6.01

Input Form

Hypergeometric2F1[-(47/8), -(9/8), 9/2, z] == (1/(9720340053765 z^(7/2))) (256 (Sqrt[z] (-536176 + 9215525 z - 92691426 z^2 + 39170569723 z^3 + 61056648792 z^4 + 4839361979 z^5 - 793172330 z^6 + 145315317 z^7 - 19498556 z^8 + 1321936 z^9) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((2144704 - 38336584 z + 395932465 z^2 - 5053927954 z^3 - 13133782553 z^4 + 13336432696 z^5 + 5218950751 z^6 - 863475290 z^7 + 154899353 z^8 - 20159524 z^9 + 1321936 z^10) Sin[ArcSin[Sqrt[z]]/4])))

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]