Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0952)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=3

http://functions.wolfram.com/07.22.03.0952.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3, 5}, -z] == (1/(1552224799125 z^3)) (64 (z (383107725 - 7151344200 z + 37743148800 z^2 + 27165650400 z^3 + 3638211840 z^4 + 147787776 z^5 + 2039808 z^6 + 8192 z^7) BesselJ[0, Sqrt[z]]^2 - 2 Sqrt[z] (766215450 - 6257426175 z + 11124199800 z^2 + 12333384000 z^3 + 1765365120 z^4 + 73135872 z^5 + 1016832 z^6 + 4096 z^7) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + 4 (383107725 + 893918025 z - 3377080350 z^2 + 6621766200 z^3 + 6362828280 z^4 + 891455616 z^5 + 36693504 z^6 + 508928 z^7 + 2048 z^8) BesselJ[1, Sqrt[z]]^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,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]