Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8b0)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8b0.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 11/4}, z] == ((2 z (1440747000 + 19823836725 z + 138572715600 z^2 - 65911104000 z^3 + 6087843840 z^4 - 156958720 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (8644482000 + 45640338975 z + 105941682000 z^2 - 62357644800 z^3 + 5991505920 z^4 - 156303360 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (-3241680750 + 10373378400 z + 37346688225 z^2 + 124203618000 z^3 - 64448524800 z^4 + 6049013760 z^5 - 156696576 z^6 + 1048576 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(182733408000 Sqrt[2] z^(11/4))

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]