Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8946)

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/07.22.03.8946.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 17/4}, z] == ((2 Sqrt[z] (-230534690411025 + 1366131498732000 z + 118183218611673600 z^2 - 171322657541038080 z^3 + 48570009586237440 z^4 - 4042880773521408 z^5 + 119405291765760 z^6 - 1296543252480 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 - 3 (-384224484018375 + 2550112130966400 z + 20400897047731200 z^2 - 134098069045248000 z^3 + 45200611739566080 z^4 - 3940287428689920 z^5 + 118277158207488 z^6 - 1292785156096 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (-1152673452055125 + 5191299695181600 z + 27733933260633600 z^2 - 138544499461939200 z^3 + 45651583567134720 z^4 - 3954590141644800 z^5 + 118437112184832 z^6 - 1293322027008 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(105217813345075200 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]