This function file computes proper integrals over interval [a,b] by enhanced midpoint integration method based on a generalization of the conventional midpoint rule. In contrast to the existing Matlab built-in functions for numerical integration, this program can be used with arrays for the upper and lower integration limits. Such an approach can save significantly computational time. Accuracy in this numerical integration is controlled by truncating integers M and N. The derivation and implementation of the numerical integration formula are shown in works [1, 2]. Some additional information can be found in the supplementary readme.pdf file.

REFERENCES
[1] S. M. Abrarov and B. M. Quine, A formula for pi involving nested radicals, Ramanujan J. 46 (3) (2018) 657-665. https://doi.org/10.1007/s11139-018-9996-8

[2] S. M. Abrarov and B. M. Quine, Identities for the arctangent function by enhanced midpoint integration and the high-accuracy computation of pi, arXiv:1604.03752 (2016). https://arxiv.org/abs/1604.03752