Citation
Fisher, Brian and Kilicman, Adem
(2010)
On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function.
Integral Transforms and Special Functions, 21 (12).
pp. 935944.
ISSN 10652469; ESSN: 14768291
Abstract
Lets F be a distribution in D' and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x)=F(x)*δn(x) for n=1, 2, … and {δn(x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ[(sinh x+)] exists and for s=0, 1, 2, … and r=1, 2, …, where M is the smallest integer greater than (s−r +1)/r and Further results are also proved.
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