Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc6h)

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=-37/8, b>=a

For fixed z and a=-37/8, b=39/8

http://functions.wolfram.com/07.23.03.bc6h.01

Input Form

Hypergeometric2F1[-(37/8), 39/8, -(11/2), z] == (1/192749568) ((1/(1 - Sqrt[z])^(23/4)) (96374784 - 554155008 Sqrt[z] + 1711200000 z - 3916868352 z^(3/2) + 7461265504 z^2 - 12515651204 z^(5/2) + 19060032219 z^3 - 26819252580 z^(7/2) + 35174537376 z^4 - 43085551872 z^(9/2) + 48940320000 z^5 - 50428105728 z^(11/2) + 43850526720 z^6 - 28058714112 z^(13/2) + 10992943104 z^7 - 1911816192 z^(15/2)) + (1/(1 + Sqrt[z])^(23/4)) (96374784 + 554155008 Sqrt[z] + 1711200000 z + 3916868352 z^(3/2) + 7461265504 z^2 + 12515651204 z^(5/2) + 19060032219 z^3 + 26819252580 z^(7/2) + 35174537376 z^4 + 43085551872 z^(9/2) + 48940320000 z^5 + 50428105728 z^(11/2) + 43850526720 z^6 + 28058714112 z^(13/2) + 10992943104 z^7 + 1911816192 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]