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Robert Reynolds
York University
LOCATION: Toronto
WEBSITE: Not indicated
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ABOUT ME:

I am a Mathematician and Technical Services Lead in the Lassonde School of Engineering at York University. I had started my PH.d in Mathematics and embarked upon publishing articles. I enjoy reading, squash, tennis and walking. My MSc. supervisor is Professor Allan Stauffer.

My supervisor and I have developed a method of evaluating the integral of the logarithm raised to an arbitrary complex power times an analytic function in terms of the Lerch function and its simplification, the Hurwitz and Riemann zeta functions. The definite integral is over an infinite domain. We evaluate the integral by expressing the integrand as a contour integral over a generalized Hankel contour and then evaluating the resulting definite integral. We use the same contour integral to express the Special Function as an infinite sum. Thus we can equate the two. This is a new method which has not been used before to our knowledge. The fact that there are well-known analytic continuations of these Special Functions allows us to extend the range of coefficients for which the integral is valid. We have used this method to generalize integrals in existing tables such as those by Gradshteyn and Ryzhik, Prudnikov et al and Bierens de Haan. In certain cases, the results involve well-known constants such as π or Catalan's constant.