Euler's Summation Method
What is the meaning of an inﬁnite sum? This question has fascinated mathematicians for a long time; from Zeno's para-dox and the series of Madhava and Leibnitz to more contem-porary times. Euler, Fourier and others played insouciantly with inﬁnite series until Abel, Cauchy and Weierstrass gave us a safe and dependable way to ``do the right thing" with in-ﬁnite series. Like other such instances in Mathematics, this did not shut the door on the older playground. Rather it pro-vided a framework to play in it with greater clarity.The author learned a lot about this the topic through the bookon $Divergent Series$ by G. H. Hardy, while teaching a course on ``Computational Methods" at IISER Mohali.
Volume 27 | Issue 6