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

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`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(13/4)}, z] == (1/(60476290875 Sqrt[2])) (z^(1/4) ((60476290875 + 138714849000 z + 113578264800 z^2 + 47850566400 z^3 + 27373731840 z^4 - 15532769280 z^5 + 19333120000 z^6 + 297795584 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-60476290875 - 90333816300 z - 45611748000 z^2 - 17255609280 z^3 - 7006648320 z^4 + 14335180800 z^5 + 1828192256 z^6 + 4194304 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 20 z (12095258175 + 8390556720 z + 3270011472 z^2 + 1325915136 z^3 - 1303400448 z^4 + 878837760 z^5 + 14680064 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]