Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afq4)

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.afq4.01

Input Form

HypergeometricPFQ[{19/4}, {3/2, -(19/4)}, z] == -((1/(228118275 z^(1/4))) (Sqrt[2] ((-228118275 + 608315400 z - 424682496 z^2 + 23924736 z^3 + 8454144 z^4 + 524288 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-76039425 + 68806080 z + 29480448 z^2 - 10092544 z^3 + 983040 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 8 z (-52971975 - 74468160 z + 14234112 z^2 + 65536 z^4) 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]