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

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=-11/4, b>=a

For fixed z and a=-11/4, b=6

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

Input Form

Hypergeometric2F1[-(11/4), 6, -(9/4), z] == (1/(491520 (-1 + z)^6)) (4 (122880 + 163840 z + 851968 z^2 + 19890176 z^3 - 150012361 z^4 + 401871377 z^5 - 551645810 z^6 + 419276154 z^7 - 168682437 z^8 + 28164213 z^9) - 231 Sqrt[1 - z] z^(13/4) (-189805 + 837375 z - 1515250 z^2 + 1394030 z^3 - 648945 z^4 + 121923 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]