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

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`=1/2

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

Input Form

HypergeometricPFQ[{19/4}, {1/2, -(19/4)}, z] == (1/(228118275 z^(1/4))) (Sqrt[2] ((228118275 - 912473100 z + 1297739520 z^2 - 521238528 z^3 + 45023232 z^4 - 17563648 z^5) BesselI[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (-228118275 + 608315400 z - 112227840 z^2 - 127905792 z^3 + 29294592 z^4 + 524288 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (228118275 + 91454400 z - 202314240 z^2 + 30277632 z^3 - 3997696 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]