Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8388)

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`=7/2

http://functions.wolfram.com/07.22.03.8388.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(13/4)}, z] == ((4 z (-2292816782025 + 3876455167200 z + 3061521619200 z^2 + 840066416640 z^3 + 155049984000 z^4 + 41844473856 z^5 - 4785700864 z^6 + 67108864 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-6878450346075 + 3303934741800 z + 1908502041600 z^2 + 481030133760 z^3 + 86972497920 z^4 + 19483066368 z^5 - 2371878912 z^6 + 33554432 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (20635351038225 - 5981261170500 z + 20243346076800 z^2 + 13368136320000 z^3 + 3550463262720 z^4 + 655060893696 z^5 + 162697052160 z^6 - 19075694592 z^7 + 268435456 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(9353666322000 Sqrt[2] z^(7/4))

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]