Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9fk)

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=35/8

http://functions.wolfram.com/07.23.03.b9fk.01

Input Form

Hypergeometric2F1[-(41/8), 35/8, 9/2, z] == (1/(532100883483 z^(7/2))) (128 ((1 + Sqrt[z])^(21/4) (-1115200 + 5854800 Sqrt[z] - 21662760 z + 61890115 z^(3/2) - 162470700 z^2 + 386416800 z^(5/2) - 1030444800 z^3 + 4756647168 z^(7/2) - 14925560832 z^4 + 25034813440 z^(9/2) - 22721986560 z^5 + 10645340160 z^(11/2) - 2027683840 z^6) + (1 - Sqrt[z])^(21/4) (1115200 + 5854800 Sqrt[z] + 21662760 z + 61890115 z^(3/2) + 162470700 z^2 + 386416800 z^(5/2) + 1030444800 z^3 + 4756647168 z^(7/2) + 14925560832 z^4 + 25034813440 z^(9/2) + 22721986560 z^5 + 10645340160 z^(11/2) + 2027683840 z^6)))

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]