Interactions of language and mathematics
Cesaro – like summation for certain divergent series
DOI:
https://doi.org/10.29051/el.v9i00.17895Keywords:
Language, Mathematics, Eulerian polynomials, Recurrence relation, Cesaro – like summationAbstract
Mathematics has its special language including grammar and symbols shared by Mathematicians universally, regardless of their mother tongue. Since mathematics is the same all across the globe, math can serve as a global language. The idea of assigning certain specific finite values to given divergent series is called Cesaro Summation. This paper attempts to analyze the interaction between mathematics and language, considering Cesaro – like summation for certain divergent series. To meet that aim, Eulerian polynomials are utilized. Also, a novel method of determining Cesaro – Like summation values by integrating particular generating functions is defined over the closed and bounded intervals for a general infinite power series whose coefficients are mth powers of natural numbers. The answers obtained provide new insights into understanding the Cesaro – Like summation process and offer a great deal of generalization and also reveal the mysterious interaction of mathematics and language.
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