Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1639)

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=3

http://functions.wolfram.com/07.22.03.1639.01

Input Form

HypergeometricPFQ[{-(5/2)}, {3, 6}, z] == -((1/(127702575 z^4)) (64 (z (680400 - 467775 z - 1984500 z^2 - 3902400 z^3 + 1506240 z^4 - 86784 z^5 + 1024 z^6) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (680400 - 382725 z - 779625 z^2 - 727200 z^3 + 360720 z^4 - 21504 z^5 + 256 z^6) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (2721600 - 1190700 z + 1743525 z^2 + 3044700 z^3 + 3211200 z^4 - 1463616 z^5 + 86272 z^6 - 1024 z^7) 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]