Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afm4)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.afm4.01

Input Form

HypergeometricPFQ[{19/4}, {-(3/2), -(19/4)}, z] == (1/(684354825 z^(1/4))) (Sqrt[2] (-3 (-228118275 + 304157700 z - 81108720 z^2 + 674150400 z^3 - 1258414080 z^4 + 785383424 z^5 + 34603008 z^6) BesselI[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (-684354825 - 69521760 z^2 + 1887621120 z^3 - 428359680 z^4 + 382205952 z^5 + 2097152 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (228118275 + 304157700 z + 370782720 z^2 + 136120320 z^3 - 106823680 z^4 - 8126464 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]