Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9k9)

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=-41/8, b>=a

For fixed z and a=-41/8, b=43/8

http://functions.wolfram.com/07.23.03.b9k9.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 11/2, z] == (1/(4552418669799 z^(9/2))) (512 ((1 + Sqrt[z])^(21/4) (-892160 + 4683840 Sqrt[z] - 16783760 z + 46643240 z^(3/2) - 115120005 z^2 + 256537820 z^(5/2) - 553864080 z^3 + 1148209920 z^(7/2) - 2679156480 z^4 + 10843728896 z^(9/2) - 32817168384 z^5 + 54544695296 z^(11/2) - 49374101504 z^6 + 23115595776 z^(13/2) - 4402970624 z^7) + (1 - Sqrt[z])^(21/4) (892160 + 4683840 Sqrt[z] + 16783760 z + 46643240 z^(3/2) + 115120005 z^2 + 256537820 z^(5/2) + 553864080 z^3 + 1148209920 z^(7/2) + 2679156480 z^4 + 10843728896 z^(9/2) + 32817168384 z^5 + 54544695296 z^(11/2) + 49374101504 z^6 + 23115595776 z^(13/2) + 4402970624 z^7)))

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]