Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4v9)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-17/8

http://functions.wolfram.com/07.23.03.b4v9.01

Input Form

Hypergeometric2F1[-(47/8), -(17/8), 11/2, z] == (1024 (-4 Sqrt[z] (-3753232 + 73121002 z - 766128482 z^2 + 6574958733 z^3 - 3158862742862 z^4 - 7485800100921 z^5 - 3371566901208 z^6 - 110144391021 z^7 + 7640122674 z^8 - 583987761 z^9 + 26273478 z^10) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((60051712 - 1211221584 z + 13057460617 z^2 - 113533156807 z^3 + 1486586933293 z^4 + 5761046612677 z^5 - 1871635047285 z^6 - 4848231174093 z^7 - 455572383921 z^8 + 31715329479 z^9 - 2388498000 z^10 + 105093912 z^11) Sin[ArcSin[Sqrt[z]]/4])))/ (12576404675444775 z^(9/2))

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]