Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9t3)

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=19/4

http://functions.wolfram.com/07.23.03.a9t3.01

Input Form

Hypergeometric2F1[-(19/4), 19/4, 7/2, -z] == (4 Sqrt[2] (-76 + 817 z - 16682 z^2 - 209799 z^3 - 693336 z^4 - 997776 z^5 - 666432 z^6 - 169728 z^7 + (1/Sqrt[1 + z]) (76 - 779 z + 16264 z^2 + 302365 z^3 + 1369902 z^4 + 2810640 z^5 + 2973984 z^6 + 1587456 z^7 + 339456 z^8)))/(672945 z^(5/2) Sqrt[-1 + Sqrt[1 + z]])

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]