Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0541)

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/07.22.03.0541.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 5}, z] == (1/(2268636244875 z^3)) (16 (z (3890016900 - 3133624725 z + 145227297600 z^2 - 355394239200 z^3 + 130553496000 z^4 - 12559958784 z^5 + 406972416 z^6 - 4714496 z^7 + 16384 z^8) BesselI[0, Sqrt[z]]^2 - 2 Sqrt[z] (7780033800 - 5294745225 z + 6051137400 z^2 - 137553292800 z^3 + 60887316960 z^4 - 6131259648 z^5 + 201732096 z^6 - 2351104 z^7 + 8192 z^8) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (15560067600 - 8644482000 z + 10697546475 z^2 - 36306824400 z^3 + 298407471840 z^4 - 124564637376 z^5 + 12359957760 z^6 - 404627456 z^7 + 4706304 z^8 - 16384 z^9) 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]