Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8c8)

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`=11/2

http://functions.wolfram.com/07.22.03.a8c8.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 7/4}, z] == ((4 z (8824575375 - 5042614500 z + 4400827200 z^2 + 149842677600 z^3 - 94384051200 z^4 + 10231971840 z^5 - 292290560 z^6 + 2097152 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (26473726125 - 10085229000 z + 10059033600 z^2 + 52483107600 z^3 - 44227814400 z^4 + 5026406400 z^5 - 145489920 z^6 + 1048576 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (79421178375 - 15127843500 z + 23628250800 z^2 - 76281004800 z^3 - 518978275200 z^4 + 367745495040 z^5 - 40638873600 z^6 + 1167065088 z^7 - 8388608 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(426377952000 Sqrt[2] z^(15/4))

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]