Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ah47)

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=-3/4, b>=a

For fixed z and a=-3/4, b=6

http://functions.wolfram.com/07.23.03.ah47.01

Input Form

Hypergeometric2F1[-(3/4), 6, -(9/4), z] == (1/(122880 (-1 + z)^8)) (4 (30720 - 184320 z + 325632 z^2 + 917504 z^3 - 3780679 z^4 + 5791463 z^5 - 5093630 z^6 + 2683846 z^7 - 791483 z^8 + 100947 z^9) - 231 Sqrt[1 - z] z^(13/4) (-7395 + 15225 z - 15950 z^2 + 9570 z^3 - 3135 z^4 + 437 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]