On defining the product r−k⋅∇lδ. (1st April 2004)

• Record Type: Journal Article
• Authors: Li, C. K.; Zou, V.
• Is Part Of: International journal of mathematics and mathematical sciences. Number 16(2004)
• Page Start: 833
• Page End: 845
• Publication Date: 2004-04-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171204305193
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Letρ ( s ) be a fixed infinitely differentiable function defined onR + = [ 0, ∞ ) having the properties: (i)ρ ( s ) ≥ 0, (ii)ρ ( s ) = 0 fors ≥ 1, and (iii)∫ R m δ n ( x ) d x = 1 whereδ n ( x ) = c m n m ρ ( n 2 r 2 ) andc m is the constant satisfying (iii). We overcome difficulties arising from computing∇ l δ n and express this regular sequence by two mutual recursions and use a Java swing program to evaluate corresponding coefficients. Hence, we are able to imply the distributional productr − k ⋅ ∇ l δ fork = 1, 2, … andl = 0, 1, 2, … with the help of Pizetti's formula and the normalization.