Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9532)

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`=7/2

http://functions.wolfram.com/07.22.03.9532.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(21/4)}, z] == ((4 z (-27812864442825 + 17831596608000 z + 7011059212800 z^2 + 847019704320 z^3 + 50502696960 z^4 + 1728053248 z^5 + 33554432 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-83438593328475 + 12304308693600 z + 3825307987200 z^2 + 440938414080 z^3 + 25819545600 z^4 + 874512384 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (250315779985425 + 10766270106900 z + 80205864076800 z^2 + 28985393203200 z^3 + 3441528668160 z^4 + 203791269888 z^5 + 6945767424 z^6 + 134217728 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (33729887646000 Sqrt[2] z^(7/4))

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]