Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acv4)

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.acv4.01

Input Form

HypergeometricPFQ[{7/4}, {-(9/2), 17/4}, z] == -((1/(8257536 Sqrt[2] z^(11/4))) (13 (2 Sqrt[z] (-3802168755 + 3706773840 z + 738855936 z^2 + 35880960 z^3 + 262144 z^4) BesselI[1/4, Sqrt[z]]^2 - 3 (-6336947925 + 10684230480 z + 3617940480 z^2 + 298287104 z^3 + 6029312 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (19010843775 + 8503775280 z + 1107532800 z^2 + 42860544 z^3 + 262144 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]