Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0913)

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=2

http://functions.wolfram.com/07.22.03.0913.01

Input Form

HypergeometricPFQ[{-(9/2)}, {2, 3}, z] == -((1/(1404728325 z)) (4 (2 z (-206288775 + 340131960 z - 96267888 z^2 + 7196544 z^3 - 165120 z^4 + 1024 z^5) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (-29469825 + 139266540 z - 45569376 z^2 + 3537216 z^3 - 82176 z^4 + 512 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (9823275 + 180912690 z - 593828784 z^2 + 185580576 z^3 - 14229504 z^4 + 329216 z^5 - 2048 z^6) BesselI[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]