Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afj4)

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`=-9/2

http://functions.wolfram.com/07.22.03.afj4.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), 17/4}, z] == -((13 (-6 Sqrt[z] (3802168755 - 3052637280 z - 1251613440 z^2 - 278446080 z^3 - 40960000 z^4 + 2097152 z^5) BesselI[1/4, Sqrt[z]]^2 + (57032531325 - 86346025920 z - 47679287040 z^2 - 10737745920 z^3 - 1931673600 z^4 - 25165824 z^5 + 8388608 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 6 Sqrt[z] (19010843775 + 11774458080 z + 3045715200 z^2 + 549765120 z^3 + 41615360 z^4 - 3145728 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1192181760 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]