Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a838)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a838.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(3/2), 19/4}, z] == ((2 Sqrt[z] (278604451125 + 173675502000 z - 32691859200 z^2 + 69093273600 z^3 + 49058611200 z^4 + 22507683840 z^5 - 9479127040 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - (835813353375 + 1794646854000 z - 203934931200 z^2 + 69189120000 z^3 + 50326732800 z^4 + 17034117120 z^5 - 9311354880 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-835813353375 - 11578366800 z - 43070227200 z^2 + 77704704000 z^3 + 51476889600 z^4 + 20242759680 z^5 - 9412018176 z^6 + 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (147220070400 Sqrt[2] z^(13/4))

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]