General Mathematics

    

Convergence Sums at Infinity with New Convergence Criteria

Authors: Chelton D. Evans, William K. Pattinson

Development of sum and integral convergence criteria, leading to a representation of the sum or integral as a point at infinity. Application of du Bois-Reymond’s comparison of functions theory, when it was thought that there were none. Known convergence tests are alternatively stated and some are reformed. Several new convergence tests are developed, including an adaption of L’Hopital’s rule. The most general, the boundary test is stated. Thereby we give an overview of a new field we call ‘Convergence sums’. A convergence sum is essentially a strictly monotonic sum or integral where one of the end points after integrating is deleted resulting in a sum or integral at a point.

Comments: 40 Pages.

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[v1] 2015-02-15 08:31:38

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