Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9y0)

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=6

http://functions.wolfram.com/07.23.03.a9y0.01

Input Form

Hypergeometric2F1[-(19/4), 6, 23/4, z] == (1/(22246588416 z^(19/4))) (-4 z^(3/4) (-337953 - 1142603 z - 3985212 z^2 - 18205572 z^3 - 5724909158 z^4 + 31205431470 z^5 - 66613236732 z^6 + 70335427932 z^7 - 36866954817 z^8 + 7688830149 z^9) + 4389 (1 - z)^(9/2) (-231 - 1771 z - 8694 z^2 - 38502 z^3 - 224595 z^4 + 1751841 z^5) Beta[z, 3/4, 1/2])

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]