Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7pu)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a7pu.01

Input Form

HypergeometricPFQ[{-(17/4)}, {1/2, 17/4}, z] == ((-2 Sqrt[z] (71641144575 - 150518768400 z - 2960748806400 z^2 + 11234822860800 z^3 - 7329079296000 z^4 + 952976277504 z^5 - 32262586368 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (119401907625 - 335772637200 z + 361686124800 z^2 + 6036910387200 z^3 - 6541103923200 z^4 + 925142876160 z^5 - 32027705344 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (358205722875 - 243145702800 z + 449902252800 z^2 + 6585313996800 z^3 - 6645296332800 z^4 + 929043578880 z^5 - 32061259776 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (3147359846400 Sqrt[2] z^(11/4))

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]