Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8950)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8950.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 21/4}, z] == ((2 Sqrt[z] (20978656827403275 - 53688967900167600 z + 113662140694502400 z^2 + 4399595652398284800 z^3 - 5613547130964541440 z^4 + 1331513435155857408 z^5 - 94300991360335872 z^6 + 2417929148694528 z^7 - 23179938496512 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]]^2 - 3 (34964428045672125 - 114345206443868400 z + 215666625933158400 z^2 + 979243058291097600 z^3 - 4573437988434739200 z^4 + 1252423350154690560 z^5 - 92219079716241408 z^6 + 2397748171112448 z^7 - 23119808954368 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (104893284137016375 - 119263279839303600 z + 358472905267276800 z^2 + 1265863840690176000 z^3 - 4700982780503654400 z^4 + 1263099618860728320 z^5 - 92510155085709312 z^6 + 2400611840557056 z^7 - 23128398888960 z^8 + 68719476736 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (3763084147870924800 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]