Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5lk)

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.b5lk.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(9/2), z] == (1/3741696) ((1/(1 + Sqrt[z])^(13/4)) (1870848 + 6080256 Sqrt[z] + 18136832 z + 39563888 z^(3/2) + 85734324 z^2 + 161005767 z^(5/2) + 314359188 z^3 + 559546416 z^(7/2) + 1111528704 z^4 + 2028778752 z^(9/2) + 5618156544 z^5 + 8877293568 z^(11/2) - 8603172864 z^6 - 38273089536 z^(13/2) - 36324507648 z^7 - 11176771584 z^(15/2)) + (1/(1 - Sqrt[z])^(13/4)) (1870848 - 6080256 Sqrt[z] + 18136832 z - 39563888 z^(3/2) + 85734324 z^2 - 161005767 z^(5/2) + 314359188 z^3 - 559546416 z^(7/2) + 1111528704 z^4 - 2028778752 z^(9/2) + 5618156544 z^5 - 8877293568 z^(11/2) - 8603172864 z^6 + 38273089536 z^(13/2) - 36324507648 z^7 + 11176771584 z^(15/2)))

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]