Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1657)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=4

http://functions.wolfram.com/07.22.03.1657.01

Input Form

HypergeometricPFQ[{-(5/2)}, {4, 5}, z] == -((1/(156080925 z^3)) (64 (z (-3586275 - 3677220 z - 5065920 z^2 + 1732800 z^3 - 91904 z^4 + 1024 z^5) BesselI[0, Sqrt[z]]^2 + 4 Sqrt[z] (1559250 + 1338345 z + 977760 z^2 - 416400 z^3 + 22784 z^4 - 256 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (1871100 + 6029145 z + 5165100 z^2 + 4265280 z^3 - 1687616 z^4 + 91392 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]