The Journal of the Indian Mathematical Society

K. B. Madhava

Abstract

Consequently, in my solution printed in Oct. 1915, I pointed out,that the result was not true for finite values of n; and making n→∞, I summed up the asymptotic series by Cesaro's first method and deduced some further results. This attracted the notice of the proposer, Prof. Sanjana, who, while agreeing with me in my method of summing the asymptotic series, regretted that there should have been an error in the binomial coefficients.

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K. B. Madhava

Abstract

The paper falls into three divisions. In the first part, which is very short, Poincare's arithmetic definition of asymptotic expansion is given. The second part emphasises the function theory and the ideas of the theory of functions of a complex variable, and contour integrals are freely used in this part; distinction is made between the different ''orders" of the asymptotic series; and integrals which may be taken to be their "sums" are obtained.

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