Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8336)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8336.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(17/4)}, z] == -(((16 z (-189172568025 - 176464008000 z - 45488390400 z^2 - 6272450560 z^3 - 636026880 z^4 - 88080384 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (764272260675 + 444375313200 z + 101693894400 z^2 + 13538242560 z^3 + 1368064000 z^4 + 170917888 z^5 - 8388608 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (-2292816782025 + 4253341276800 z + 3067470201600 z^2 + 758222438400 z^3 + 103330283520 z^4 + 10502537216 z^5 + 1392508928 z^6 - 67108864 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2007731407500 Sqrt[2] z^(3/4)))

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]