Pascal’s Triangle and Bernoulli Numbers: Applications in Scientific Computing
Keywords:
Approximation, Bernoulli Numbers, Numerical Computation, Pascal’s Triangle, Recursive Algorithms.Abstract
Bernoulli numbers are the key concept in number theory. Such a number first appeared in Jakob Bernoulli's famous book Ars Conjectandi. These are used in the Euler-Maclaurin summation formula. Such a formula helps with the fast computation of the slowly converging series. Bernoulli numbers and the world-famous Pascal’s triangle are closely related. Here, the focus is on their formulations, properties, and interconnections related to information technology, computer science, and scientific computing to explore and highlight how they improve the algorithm efficiency, computational speed, and memory optimization.
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