Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7v2)

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`=9/2

http://functions.wolfram.com/07.22.03.a7v2.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 13/4}, z] == -(((2 z (-2417625014805 - 23400734220864 z + 24538131991296 z^2 - 4346198360064 z^3 + 219043921920 z^4 - 3602907136 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (-3857353575075 - 7146756096480 z + 21036239288064 z^2 - 4159744917504 z^3 + 215916150784 z^4 - 3588227072 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 (645080436000 + 4863224190825 z + 8695463736960 z^2 - 21483647767296 z^3 + 4185411452928 z^4 - 216358256640 z^5 + 3590324224 z^6 - 16777216 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(18558639171072 Sqrt[2] z^(9/4)))

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]