Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.am5f)

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, b>=a

For fixed z and a=3, b=21/4

http://functions.wolfram.com/07.23.03.am5f.01

Input Form

Hypergeometric2F1[3, 21/4, -(19/4), z] == (1/(46189 (-1 + z)^13)) (-46189 + 753610 z - 6104241 z^2 + 34035768 z^3 - 161669898 z^4 + 970019388 z^5 + 8891844390 z^6 + 7113475512 z^7 + 889184439 z^8 - 15199734 z^9 + 447051 z^10)

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]