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

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=-19/8, b>=a

For fixed z and a=-19/8, b=25/8

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

Input Form

Hypergeometric2F1[-(19/8), 25/8, 7/2, z] == (1/(3309033 z^(5/2))) (32 ((1 + Sqrt[z])^(11/4) (-3344 + 9196 Sqrt[z] - 24035 z + 45980 z^(3/2) - 117040 z^2 + 277760 z^(5/2) - 295680 z^3 + 107520 z^(7/2)) + (1 - Sqrt[z])^(11/4) (3344 + 9196 Sqrt[z] + 24035 z + 45980 z^(3/2) + 117040 z^2 + 277760 z^(5/2) + 295680 z^3 + 107520 z^(7/2))))

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]