Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5sm)

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=47/8

http://functions.wolfram.com/07.23.03.b5sm.01

Input Form

Hypergeometric2F1[-(47/8), 47/8, -(9/2), z] == (1/(64512 (1 - z)^(9/2))) (-4 Sqrt[1 - z] (-16128 - 58688 z - 192225 z^2 - 711667 z^3 - 3658963 z^4 - 46998039 z^5 + 542446542 z^6 - 1581243840 z^7 + 2037619584 z^8 - 1237065984 z^9 + 289884672 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (16128 + 53648 z + 171743 z^2 + 642554 z^3 + 3405655 z^4 + 830082792 z^5 - 4577436072 z^6 + 9854152704 z^7 - 10479667968 z^8 + 5528033280 z^9 - 1159538688 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]