Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1661)

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/07.22.03.1661.01

Input Form

HypergeometricPFQ[{-(5/2)}, {4, 6}, z] == -((1/(468242775 z^4)) (128 (2 z (-935550 - 6081075 z - 4166100 z^2 - 4132800 z^3 + 1177920 z^4 - 52992 z^5 + 512 z^6) BesselI[0, Sqrt[z]]^2 + Sqrt[z] (7484400 + 19178775 z + 11499300 z^2 + 6667200 z^3 - 2278080 z^4 + 105216 z^5 - 1024 z^6) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + 2 (-3742200 + 5145525 z + 8907300 z^2 + 5498100 z^3 + 3582000 z^4 - 1151808 z^5 + 52736 z^6 - 512 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]