In this study, it is proved that the neutrix composition δ(s)[(sinh−1x+)r] δ ( s ) [ ( sinh - 1 x + ) r ] exists and is given by δ(s)[(sinh−1x+)r]=sr+r−1∑k=0k∑i ...

Jun 1, 2011 · 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( ...

PDF | Let $F$ be a distribution in $\mathcal{D}'$ and let $f$ be a locally summable function. The composition $F(f(x))$ of $F$ and $f$ is said to exist.

Note that taking the neutrix limit of a function f n is equivalent to taking the usual limit of Hadamard's finite part of f n . The definition of the neutrix ...

It is proved that the neutrix composition δ(rs-1)((tanhx) = F(f(x)) is equal to h(x), where Fn(x)=F(x)*δn(x) for n=1,2,… and {δ n(x)} is a certain regular ...

Dec 4, 2013 · 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 {F[subscript n](f(x))} is ...

In this study, it is proved that the neutrix composition δ(s)[(sinh⁡-1x+)r] exists and is given by δ(s)[(sinh⁡-1x+)r]=∑k=0sr+r-1∑i=0k(ki)((-1)krcs,k,i/2k+1k!)

On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function. Brian Fisher Department of Mathematics ...

On the neutrix composition of the delta and inverse hyperbolic sine functions. Citation metadata. Authors: Brian Fisher and Adem Kilicman. Date: Annual 2011.

In this study, it is proved that the neutrix composition exists and is given by, for and , where . Let be a distribution in and let be a locally summable ...