Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0875)

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=1

http://functions.wolfram.com/07.22.03.0875.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1, 3}, z] == -((1/(127702575 z)) (4 (4 z (-8037225 + 24590790 z - 11056104 z^2 + 1147680 z^3 - 33792 z^4 + 256 z^5) BesselI[0, Sqrt[z]]^2 + Sqrt[z] (893025 - 71702820 z + 40999104 z^2 - 4491072 z^3 + 134400 z^4 - 1024 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (-893025 + 5358150 z - 79305624 z^2 + 42027264 z^3 - 4523904 z^4 + 134656 z^5 - 1024 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]