Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0529)

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

For fixed z and a₁=-11/2, b₁=1

http://functions.wolfram.com/07.22.03.0529.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 2}, z] == (1/1404728325) ((1404728325 - 6528392640 z + 4801286304 z^2 - 840648960 z^3 + 45149952 z^4 - 806912 z^5 + 4096 z^6) BesselI[0, Sqrt[z]]^2 + 4 Sqrt[z] (995019795 - 1059834744 z + 202026672 z^2 - 11137920 z^3 + 200960 z^4 - 1024 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (-108056025 + 4640003856 z - 4412447136 z^2 + 818666496 z^3 - 44749568 z^4 + 804864 z^5 - 4096 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]