Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9504)

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`=5/2

http://functions.wolfram.com/07.22.03.9504.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, -(1/4)}, z] == (1/(730957500 Sqrt[2] z^(3/4))) ((8 z (99434475 + 821847600 z - 1004194800 z^2 + 168631040 z^3 - 6819840 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (48388725 + 408366000 z - 909493200 z^2 + 164478720 z^3 - 6778880 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (145166175 - 940123800 z - 5002704000 z^2 + 7716643200 z^3 - 1335613440 z^4 + 54427648 z^5 - 524288 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]