Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.am5d)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=4, a₃>=4

For fixed z and a₁=-1/2, a₂=4, a₃=4

For fixed z and a₁=-1/2, a₂=4, a₃=4, b₁=-5/2

http://functions.wolfram.com/07.27.03.am5d.01

Input Form

HypergeometricPFQ[{-(1/2), 4, 4}, {-(5/2), 1/2}, -z] == (3840 + 19784 z - 64644 z^2 - 1820781 z^3 + 1867556 z^4 - 221076 z^5)/ (3840 (1 + z)^9) + (1/(768 (1 + z)^(19/2))) (7 (-280 Sqrt[z] - 2660 z^(3/2) - 11305 z^(5/2) + 63758 z^(7/2) - 34424 z^(9/2) + 2288 z^(11/2)) ArcSinh[Sqrt[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},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},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]