Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9r3)

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=-27/8

http://functions.wolfram.com/07.23.03.b9r3.01

Input Form

Hypergeometric2F1[-(39/8), -(27/8), 21/4, z] == (1/(12718861322825 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4004208 - 86475492 z + 1041284451 z^2 - 11147054121 z^3 + 312456608919 z^4 + 1679112658979 z^5 + 1941702703449 z^6 + 624499580853 z^7 + 44434371197 z^8 - 93663243 z^9 + (1/Sqrt[1 - z]) (-4004208 + 88477596 z - 1084021671 z^2 + 11657137173 z^3 - 317905223727 z^4 - 1126751508127 z^5 + 57669864383 z^6 + 1051182410207 z^7 + 314063384619 z^8 + 11208368079 z^9 - 124884324 z^10)))

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]