Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a98n)

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=-5/4

http://functions.wolfram.com/07.23.03.a98n.01

Input Form

Hypergeometric2F1[-(19/4), -(5/4), -(7/2), z] == (1/224) ((1 - Sqrt[z])^(5/2) (112 + 280 Sqrt[z] + 300 z + 260 z^(3/2) + 215 z^2 + 156 z^(5/2) + 100 z^3 + 40 z^(7/2)) + Sqrt[1 + Sqrt[z]] (112 - 56 Sqrt[z] - 148 z + 60 z^(3/2) - 5 z^2 + 14 z^(5/2) + 3 z^3 + 4 z^(7/2) + 20 z^4 - 40 z^(9/2)))

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]