Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4632)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-17/3, b>=a

For fixed z and a=-17/3, b=-7/3

http://functions.wolfram.com/07.23.03.4632.01

Input Form

Hypergeometric2F1[-(17/3), -(7/3), 11/2, -z] == -((6561 (Sqrt[z] (37158912 + 750649344 z + 8142520320 z^2 + 71869923328 z^3 - 4988760132653 z^4 + 4705093546905 z^5 + 6321534648926 z^6 - 3399307223080 z^7 + 39815481792 z^8 + 2460792448 z^9 + 98011648 z^10) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-111476736 - 2218917888 z - 23784783872 z^2 - 208845930496 z^3 - 2862331265024 z^4 + 21759383733263 z^5 - 24888247073882 z^6 + 5736909530792 z^7 + 38621839936 z^8 + 2411786624 z^9 + 98011648 z^10) Sinh[ArcSinh[Sqrt[z]]/3]))/ (39120021629013325 z^(9/2) Sqrt[1 + z]))

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]