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Ganapathi Iyer, V.
- Rearrangement of Complex Series
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The Journal of the Indian Mathematical Society, Vol 1 (1935), Pagination: 8-22Abstract
This is an attempt at an exhaustive classification of infinite series whose terms are complex numbers, according to the manner of distribution of the limiting values of the series when the terms of the series are re-arranged so as to form another series. By the limiting values of the series are meant the limit points of the sequence obtained by taking the sum to first n terms of the series in any particular rearrangement. A definite arrangement of the terms of the series being presupposed, the series converges or diverges according as the sequence has a unique finite or infinite limit; otherwise the series oscillates.- Tauberian Theorems on Generalised Lambert's Series
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The Journal of the Indian Mathematical Society, Vol 1 (1935), Pagination: 73-87Abstract
In what follows it is supposed that the half-plane of convergence is σ>0 and that s=ξ→0 through positive real values. The object of this paper is to prove for the series (1) the analogue of the following theorems for Dirichlets' series.- A Note on the Values of an Analytic Function near an Essential Singularity
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1 Madras University, IN
1 Madras University, IN