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- W1989527073 abstract "Using the operations of the fractional calculus, the chemically important sum $ - Sigma ( - 1)^j j^{{1 /2}} exp (jx)$ is proved equivalent to $Sigma beta ^{ - 3} [pi {{(beta - x)} /2}]^{{1 /2}} [beta + 2x]$ where $beta = [(2j - 1)^2 pi ^2 + x^2 ]^{{1 /2}} $ and where, in each summation, j runs from 1 to $infty $. Seven other sums of exponential functions are similarly reformulated, as well as eight summations of sine or cosine functions, of which $Sigma j^{{{ - 1} /2}} sin (jpi x)$ is representative. The utility of these reformulations is demonstrated." @default.
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- W1989527073 date "1983-09-01" @default.
- W1989527073 modified "2023-09-25" @default.
- W1989527073 title "The Reformulation of an Infinite Sum via Semiintegration" @default.
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- W1989527073 doi "https://doi.org/10.1137/0514076" @default.
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