Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9136)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9136.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 15/4}, z] == ((2 Sqrt[z] (-767555262849375 - 478476008010000 z + 281038421664000 z^2 + 97381463961600 z^3 + 10513185177600 z^4 + 558225162240 z^5 + 16693329920 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - (-2302665788548125 - 4944252082770000 z + 369581468256000 z^2 + 105125948928000 z^3 + 10893238272000 z^4 + 569109381120 z^5 + 16861102080 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (2302665788548125 + 31898400534000 z + 310917743136000 z^2 + 100263550464000 z^3 + 10659756441600 z^4 + 562503352320 z^5 + 16760438784 z^6 + 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(510117543936000 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]