Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aj8i)

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=21/4

http://functions.wolfram.com/07.23.03.aj8i.01

Input Form

Hypergeometric2F1[3/4, 21/4, -(3/2), -z] == (1/(884 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((2 (221 + 2210 z + 72598 z^2 + 9708 z^3 + 4153 z^4 + 1130 z^5 + 140 z^6))/(1 + z)^(15/2) - (-442 - 4199 z + 83979 z^2 + 35439 z^3 + 15587 z^4 + 4380 z^5 + 560 z^6)/(1 + z)^7))

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]