Estimating the number of Prime numbers less than a given positive integer by a novel quadrature method: A study of Accuracy and Convergence.
|Title||Estimating the number of Prime numbers less than a given positive integer by a novel quadrature method: A study of Accuracy and Convergence.|
|Publication Type||Conference Paper|
|Year of Publication||2014|
|Authors||A. Ahamed, M., and S.. Saha|
|Editor||S., M., K. D., M. P., C. D.E., M. B., S. A., and T. S.M.|
|Conference Name||3rd International Conference on Advances in Computing, Communications and Informatics, ICACCI 2014|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|ISBN Number||9781479930791 (ISBN)|
|Keywords||Analytical results, Computation theory, Degree of Accuracy, Improper integrals, Logarithmic integral, Number theory, Numerical integrations, Quadrature formula, Quadrature methods, Trapezoidal rules|
The role of Numerical Integration in the evaluation of definite improper integrals is being increasingly appreciated as there are no simple analytical results available. In this paper the authors explore four such quadrature formulae and their performance in evaluating Logarithmic integrals, a class of definite improper integrals and one of the important integrals in Number Theory. The performance of the proposed methods are compared with some well known quadrature formulae like Simpson's rule, Trapezoidal rule , Weddle's rule etc. © 2014 IEEE.