On the convolution and neutrix convolution of the functions $\boldsymbol{\sinh^{-1}x}$ and $\boldsymbol{x^r}$

Authors

Brian Fisher University of Leicester, Department of Mathematics, Leicester, UK
Fatma Al-Sirehy King Abdulaziz University, Department of Mathematics, Jeddah, Saudi Arabia

Convolution, neutrix convolution, neutrix limit

The neutrix convolution $\sinh^{-1}x \circledast x^r$ is evaluated for $r=0,1,2,\ldots .$ Further results are also given.

Abstract: 29 / PDF: 8

[1] J. G. van der Corput, Introduction to the neutrix calculus, J. Analyse Math., 7 (1959--1960), 291--398.

[2] B. Fisher, Neutrices and the convolution of distributions, Univ. of Novi Sad, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat, 17 (1987), 119--135.

[3] B. Fisher and B. Jolevska-Tuneska, On the logarithmic integral, Hacet. J. Math. Stat., 39 (3) (2010), 393-401.

[4] B. Fisher, M. Telci and F. Al-Sirehy) The error function and the neutrix convolution, Internat. J. Appl. Math., 8 (3) (2002), 295--309.

[5] B. Jolevska-Tuneska and B. Fisher, On the logarithmic integral and convolutions, Bull. Malaysa. Math. Sci., (2) 37 (3) (2012), 671--677.

[6] B. Jolevska-Tuneska, B. Fisher and E. Özçağ, On the dilogarithm integral, Int. J. Appl. Math., 24 (3) (2011), 361--369.

[7] B. Fisher and J. D. Nicholas, The exponential integral and the convolution, SUT J. Math., 33 (2) (1997), 139-148.

[8] B. Fisher and J. D. Nicholas, On the exponential integral, Hacet. Bull. Nat. Sci. Eng. Ser. B, 28 (1999), 55--64.

[9] I. M. Gel'fand and G.E. Shilov, Generalized Function, Vol. I, Academic Press, 1964.

[10] M. Lin, B. Fisher and S. Orankitjaroen, On the non-commutative neutrix convolution of $tan^{-1}x$ and $x^r$, Math. Moravica, to appear.