Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9931)

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=-23/4, b>=a

For fixed z and a=-23/4, b=4

http://functions.wolfram.com/07.23.03.9931.01

Input Form

Hypergeometric2F1[-(23/4), 4, -(21/4), z] == (1/(7128576 (-1 + z)^4)) (4 (1782144 + 678912 z + 1277952 z^2 + 2798592 z^3 + 7749632 z^4 + 33090560 z^5 + 587104256 z^6 - 3155027691 z^7 + 5318190801 z^8 - 3783392613 z^9 + 985747455 z^10) - 100947 Sqrt[1 - z] z^(25/4) (-11803 + 32967 z - 30969 z^2 + 9765 z^3) 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]