Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4558)

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=-16/3

http://functions.wolfram.com/07.23.03.4558.01

Input Form

Hypergeometric2F1[-(17/3), -(16/3), 9/2, -z] == (243 ((-Sqrt[z]) (452984832 + 14831058944 z + 317961797632 z^2 - 90817637283241 z^3 + 442910766610939 z^4 - 313996618346764 z^5 - 405895668113840 z^6 + 371583575008256 z^7 - 68242294634240 z^8 + 2307068208128 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + 9 Sqrt[1 + z] (150994944 + 4898947072 z + 104555610112 z^2 + 3410472468480 z^3 - 64797095994763 z^4 + 226151811675812 z^5 - 254878580292048 z^6 + 100816697684224 z^7 - 12547083747584 z^8 + 318346503168 z^9) Sinh[ArcSinh[Sqrt[z]]/3]))/ (24577042592149355 z^(7/2) 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]