On defining the product r − k ⋅ ∇ l δ

C. K. Li and V. Zou

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-13

Abstract:

Let ρ ( s ) be a fixed infinitely differentiable function defined on R + = [ 0 , ∞ ) having the properties: (i) ρ ( s ) ≥ 0 , (ii) ρ ( s ) = 0 for s ≥ 1 , and (iii) ∫ R m δ n ( x ) d x = 1 where δ n ( x ) = c m n m ρ ( n 2 r 2 ) and c 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 product r − k ⋅ ∇ l δ for k = 1 , 2 , … and l = 0 , 1 , 2 , … with the help of Pizetti's formula and the normalization.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:347591

DOI: 10.1155/S0161171204305193

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