Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9054)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9054.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(19/4)}, z] == ((-4 z (162162759212078625 - 12800492361657000 z + 966357653788800 z^2 + 2471285288908800 z^3 + 405849667829760 z^4 + 31148119425024 z^5 + 1496133402624 z^6 + 53552873472 z^7 + 2147483648 z^8) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (270271265353464375 + 2689958539768500 z + 2106820674504000 z^2 + 1444579068441600 z^3 + 217909330329600 z^4 + 16275190579200 z^5 + 773081530368 z^6 + 27715960832 z^7 + 1073741824 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-4054068980301965625 - 400711065234480000 z - 22868863823988000 z^2 + 13567824938304000 z^3 + 11251885420339200 z^4 + 1723587025305600 z^5 + 129317637980160 z^6 + 6153647947776 z^7 + 220653944832 z^8 + 8589934592 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(3856717202738400 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]