Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ak24)

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=5/4, b>=a

For fixed z and a=5/4, b=5

http://functions.wolfram.com/07.23.03.ak24.01

Input Form

Hypergeometric2F1[5/4, 5, -(17/4), z] == (1/(28288 (-1 + z)^11)) (4 (-7072 + 88192 z - 524960 z^2 + 2049280 z^3 - 6533600 z^4 + 38425216 z^5 - 23101671 z^6 - 12012154 z^7 + 1850156 z^8 - 251174 z^9 + 17787 z^10) - 231 Sqrt[1 - z] z^(21/4) (-295075 - 47212 z + 7326 z^2 - 1036 z^3 + 77 z^4) 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]