Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9632)

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/07.22.03.9632.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(17/4)}, z] == ((4 z (-34070758942460625 + 556257288856500 z - 388517868446400 z^2 + 292093186176000 z^3 + 85468126003200 z^4 + 9002519101440 z^5 + 543434997760 z^6 + 23420993536 z^7 + 1073741824 z^8) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-102212276827381875 - 17800233243408000 z + 163684591408800 z^2 + 187147016179200 z^3 + 46223786188800 z^4 + 4696998543360 z^5 + 279938334720 z^6 + 12046041088 z^7 + 536870912 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (306636830482145625 + 111807715060156500 z + 6646377412659600 z^2 - 952196064019200 z^3 + 1275070538649600 z^4 + 351976660992000 z^5 + 36598012968960 z^6 + 2198838706176 z^7 + 94757715968 z^8 + 4294967296 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(498070359072000 Sqrt[2] z^(15/4))

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]