Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ek)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-19/4, b>=a

For fixed z and a=-19/4, b=3/4

http://functions.wolfram.com/07.23.03.a9ek.01

Input Form

Hypergeometric2F1[-(19/4), 3/4, 7/2, z] == (1/(672945 z^(5/2))) (4 ((1 + Sqrt[z])^(15/2) (2508 - 18810 Sqrt[z] + 58729 z - 94050 z^(3/2) + 87780 z^2 - 48832 z^(5/2) + 15120 z^3 - 2016 z^(7/2)) - (1 - Sqrt[z])^(15/2) (2508 + 18810 Sqrt[z] + 58729 z + 94050 z^(3/2) + 87780 z^2 + 48832 z^(5/2) + 15120 z^3 + 2016 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]