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

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=-39/8, b>=a

For fixed z and a=-39/8, b=31/8

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

Input Form

Hypergeometric2F1[-(39/8), 31/8, 9/2, z] == (1/(5435418483 z^(7/2))) (256 ((-Sqrt[z]) (-32240 - 45539 z - 145483 z^2 - 22639529 z^3 + 102100031 z^4 - 185767560 z^5 + 171069008 z^6 - 79573824 z^7 + 14927616 z^8) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((128960 + 93496 z + 446121 z^2 + 5209581 z^3 - 58460237 z^4 + 177990439 z^5 - 262288312 z^6 + 208989968 z^7 - 87037632 z^8 + 14927616 z^9) 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]