Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9339)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=3, a₃>=3

For fixed z and a₁=-7/2, a₂=3, a₃=7/2

For fixed z and a₁=-7/2, a₂=3, a₃=7/2, b₁=-5/2

http://functions.wolfram.com/07.27.03.9339.01

Input Form

HypergeometricPFQ[{-(7/2), 3, 7/2}, {-(5/2), -(5/2)}, -z] == (1/(25 (1 + z)^8)) (25 + 347 z + 3346 z^2 + 98126 z^3 + 1830997 z^4 + 7891415 z^5 + 18035584 z^6 + 24793472 z^7 + 21343872 z^8 + 11324544 z^9 + 3400320 z^10 + 443520 z^11) + (88704/5) z^(7/2) ArcTan[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]