Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9240)

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`=-7/2

http://functions.wolfram.com/07.22.03.9240.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 23/4}, z] == -(((2 Sqrt[z] (379939855110440625 + 317548577315970000 z - 13727311678080000 z^2 + 3003582726144000 z^3 - 2534635605196800 z^4 - 852552843264000 z^5 - 109951498321920 z^6 - 9159017758720 z^7 - 785979015168 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 + (-1139819565331321875 - 2689513641024210000 z - 183382804725120000 z^2 - 2252687044608000 z^3 + 3245629685760000 z^4 + 935073467596800 z^5 + 116196649205760 z^6 + 9534827397120 z^7 + 743029342208 z^8 - 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (1139819565331321875 + 257898568317390000 z + 3731012917632000 z^2 - 2021642219520000 z^3 + 2799590208307200 z^4 + 883784259993600 z^5 + 112421775605760 z^6 + 9328668966912 z^7 + 768799145984 z^8 - 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(4484912224665600 Sqrt[2] z^(17/4)))

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]