Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8wk)

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

For fixed z and a₁=-11/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a8wk.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(7/2), 19/4}, z] == ((2 Sqrt[z] (897725453625 + 733296564000 z - 37050773760 z^2 + 28096839680 z^3 + 6860242944 z^4 + 522190848 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (2693176360875 + 6303777480000 z + 341690469120 z^2 + 33456783360 z^3 + 7214792704 z^4 + 532676608 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-2693176360875 - 558334576800 z - 26072766720 z^2 + 30046765056 z^3 + 6997344256 z^4 + 526385152 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(45801799680 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]