Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.4597)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=4, b_1`>=-11/2

For fixed z and a₁=4, b₁=-9/2

http://functions.wolfram.com/07.22.03.4597.01

Input Form

HypergeometricPFQ[{4}, {-(9/2), 6}, -z] == (1/(378 z^5)) (103378275 (38 + z) + (-3928374450 + 7753370625 z - 2412159750 z^2 + 280269990 z^3 - 15752880 z^4 + 452544 z^5 - 5120 z^6) Cos[2 Sqrt[z]] - 2 Sqrt[z] (3928374450 - 2515538025 z + 454864410 z^2 - 36100350 z^3 + 1458600 z^4 - 28224 z^5 + 128 z^6) Sin[2 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,a₂},{b₁},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]