Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5lj)

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=37/8

http://functions.wolfram.com/07.23.03.b5lj.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(19/4), z] == (1/(1357664 2^(3/4) (-1 + z)^3)) ((1 + Sqrt[1 - z])^(3/4) (-678832 - 1973972 z - 4990755 z^2 - 13615413 z^3 - 47409780 z^4 + 8571188736 z^5 - 25306051584 z^6 + 25184501760 z^7 - 8382578688 z^8 + (1/Sqrt[1 - z]) (-678832 - 1634556 z - 3918915 z^2 - 10830862 z^3 - 39828339 z^4 - 9164819664 z^5 + 39324688128 z^6 - 62050222080 z^7 + 43126161408 z^8 - 11176771584 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]