Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad8q)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ad8q.01

Input Form

HypergeometricPFQ[{9/4}, {-(11/2), -(21/4)}, z] == (1/(10854718875 Sqrt[2])) (z^(1/4) ((10854718875 + 22555260000 z + 14789174400 z^2 + 3419020800 z^3 + 472158720 z^4 + 55664640 z^5 + 22937600 z^6 + 2097152 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-10854718875 - 13871484900 z - 4463877600 z^2 - 739333440 z^3 - 88888320 z^4 - 12042240 z^5 + 9699328 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (10854718875 + 5187709800 z + 1085600880 z^2 + 144754560 z^3 + 17049600 z^4 + 3440640 z^5 + 524288 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]