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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(19/4)}, z] == -((Sqrt[2] ((-45054499903875 + 80192698393500 z - 12186990723600 z^2 - 17479666512000 z^3 - 5622161529600 z^4 - 1478007336960 z^5 + 7067253473280 z^6 + 8011659608064 z^7 + 227247390720 z^8 + 268435456 z^9) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-15018166634625 + 6706677285000 z + 8694043696800 z^2 + 3137580230400 z^3 + 743250816000 z^4 + 77662126080 z^5 + 1558197043200 z^6 + 295832649728 z^7 + 2080374784 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-45054499903875 - 39952634683500 z - 15745635813600 z^2 - 4208657745600 z^3 - 1155830860800 z^4 - 770149416960 z^5 + 1375870648320 z^6 + 52181336064 z^7 + 67108864 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(45054499903875 z^(1/4)))

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]