Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3w7)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=11/8, b>=a

For fixed z and a=11/8, b=47/8

http://functions.wolfram.com/07.23.03.c3w7.01

Input Form

Hypergeometric2F1[11/8, 47/8, -(13/4), z] == (1/(1334736 2^(1/4) (-1 + z)^10)) ((1 + Sqrt[1 - z])^(1/4) (4 (166842 - 2072691 z + 13033640 z^2 - 63622416 z^3 - 615188754 z^4 - 38214895 z^5 + 8678424 z^6 - 1448550 z^7 + 120176 z^8) + (1/Sqrt[1 - z]) (667368 - 8624448 z + 56196521 z^2 - 279562309 z^3 + 7938233490 z^4 + 4042881590 z^5 - 705075811 z^6 + 154631103 z^7 - 24498736 z^8 + 1922816 z^9)))

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]