ON THE CONVOLUTION AND NEUTRIX CONVOLUTION
INVOLVING THE FUNCTIONS cosh-1x, sinh-1x AND xr
Abstract. The domain of the function $\cosh^{-1}x$ is extended to the real line by putting $\cosh^{-1}x =0$ on the interval $(-1,1).$ The neutrix convolution $\cosh^{-1}x \circledast x^r$ and $\sinh^{-1}x \circledast x^r$ are evaluated for $r=0,1,2,\ldots .$ Further results are also given.
AMS Subject classification: 33B15, 33B20, 46F10


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DOI: 10.12732/ijam.v27i6.6

Volume: 27
Issue: 6
Year: 2014