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

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=13/4, b>=a

For fixed z and a=13/4, b=6

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

Input Form

Hypergeometric2F1[13/4, 6, -(9/4), z] == (1/(7680 (-1 + z)^12)) (4 (1920 - 39680 z + 524416 z^2 - 14985728 z^3 - 42554807 z^4 + 21585319 z^5 + 33294850 z^6 + 2286438 z^7 - 117579 z^8 + 4851 z^9) - 231 Sqrt[1 - z] z^(13/4) (189805 + 502425 z + 239250 z^2 + 9570 z^3 - 495 z^4 + 21 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]