On defining the productr−k⋅∇lδ
2004 ◽
Vol 2004
(16)
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pp. 833-845
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Keyword(s):
Letρ(s)be a fixed infinitely differentiable function defined onR+=[0,∞)having the properties: (i)ρ(s)≥0, (ii)ρ(s)=0fors≥1, and (iii)∫Rmδn(x)dx=1whereδn(x)=cmnmρ(n2r2)andcmis the constant satisfying (iii). We overcome difficulties arising from computing∇lδnand 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⋅∇lδfork=1,2,…andl=0,1,2,…with the help of Pizetti's formula and the normalization.
2007 ◽
Vol 18
(5)
◽
pp. 337-350
1976 ◽
Vol 17
(1)
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pp. 53-56
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1972 ◽
Vol 72
(2)
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pp. 201-204
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Keyword(s):
1988 ◽
Vol 21
(3)
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pp. 383-386
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1990 ◽
Vol 151
(1)
◽
pp. 17-19
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1998 ◽
Vol 89
(1)
◽
pp. 53-72
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