Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa4c)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa4c.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, 11/4}, z] == (1/(7072000 Sqrt[2] z^(15/4))) ((4 z (-540225 + 396900 z + 1266300 z^2 + 3181760 z^3 - 629760 z^4 + 16384 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-1620675 + 882000 z + 1193850 z^2 + 1407840 z^3 - 309760 z^4 + 8192 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (4862025 - 1719900 z + 4410000 z^2 + 7383600 z^3 + 12122880 z^4 - 2502656 z^5 + 65536 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]