Approximation of Euler Number Using Gamma Function
Shekh Zahid, Prasanta Kumar Ray · American Journal of Undergraduate Research · 2015
This research presents a formula to calculate Euler number using gamma function. The representation is somewhat similar to Taylor series expansion of e. The number e is presented as sum of an integral and decimal part. But it is well known that e is an irrational number, and therefore such an expression for e does not exist in principle, that is why we are approximately representing it for use in computation. The approximation of our formula increases as we increase the value of index in the summation formula. We also analyse the approximation of our formula by both numerical and graphical methods. KEYWORDS: Euler Number, Gamma Function, Approximation, Computing, L’Hospital's Rule