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

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=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, 13/4, z] == (1/(183230845 z^3)) (4 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (14260 + 271653 z + 14650011 z^2 - 171319428 z^3 + 614693376 z^4 - 976389120 z^5 + 718602240 z^6 - 200540160 z^7 - (1/Sqrt[1 - z]) (14260 + 264523 z + 14512402 z^2 - 201583137 z^3 + 898913040 z^4 - 1904302848 z^5 + 2111324160 z^6 - 1186529280 z^7 + 267386880 z^8)))

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]