Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af4m)

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`=-7/2

http://functions.wolfram.com/07.22.03.af4m.01

Input Form

HypergeometricPFQ[{17/4}, {-(7/2), 23/4}, z] == (209 (-2 Sqrt[z] (5771092201875 + 6502263768000 z + 1331261568000 z^2 + 117478932480 z^3 + 5393612800 z^4 + 113246208 z^5) BesselI[-(1/4), Sqrt[z]]^2 + (17313276605625 + 45888927084000 z + 15079611456000 z^2 + 1866546339840 z^3 + 114942935040 z^4 + 3688890368 z^5 + 33554432 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (17313276605625 + 8953936992000 z + 1606068172800 z^2 + 133534679040 z^3 + 5885657088 z^4 + 117440512 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1635778560 Sqrt[2] z^(17/4))

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]