Srivastava, H.M.Nishimoto, Katsuyuki2010-05-192010-05-1919942010-05-19http://hdl.handle.net/1828/2781In the remarkably vast literature on fractional calculus, there are many systematic (and historical) accounts of its applications in a number of areas including (for example) ordinary and partial differential equations, special functions, and summation of series. The object of the present note is to examine rather closely some of the most recent contributions by K. Nishimoto [2] on the use of fractional calculus of logarithmic functions in deriving numerous interesting infinite sums. Some generalizations and relevant connections with certain familiar results in the theory of the Gaussian hypergeometric function are also given.enfractional calculusordinary and partial differential equationsspecial functionssummation of serieslogarithmic functionsGaussian hypergeometric functionfractional differintegralsgeneralized hypergeometric functionsbinomial expansionmathematical inductionaugmentation of parametersLaplace and inverse Laplace transformstechnical reports (mathematics and statistics)Technical ReportDepartment of Mathematics and Statistics