Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9o9)

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=-35/8

http://functions.wolfram.com/07.23.03.b9o9.01

Input Form

Hypergeometric2F1[-(39/8), -(35/8), 17/4, z] == (1/(84626474555 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4 (-38502 + 1067361 z - 20213550 z^2 + 923220207 z^3 + 7754942632 z^4 + 14447325615 z^5 + 8249765778 z^6 + 1395136801 z^7 + 48250938 z^8) + (1/Sqrt[1 - z]) (154008 - 4346448 z + 82969671 z^2 - 3732783873 z^3 - 23894021405 z^4 - 16932558341 z^5 + 24074251573 z^6 + 18053401149 z^7 + 2321712585 z^8 + 31221081 z^9)))

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]