ON THE GENERALIZED FRESNEL SINE INTEGRALS AND CONVOLUTION

The generalized Fresnel sine integral Sk(x) and its associated functions Sk+(x) ; Sk-(x) are de�fined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the generalized Fresnel sine integral and its associated functions are then found

SOME RESULTS ON COLOMBEAU PRODUCT OF DISTRIBUTIONS

In this paper some results on singular products of distributions are derived. The results are obtained in Colombeau algebra of generalized functions, which is most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions

The Guideline of MathSTEM Method: Teaching Mathematics in STEM Context for STEM Students

This is a teaching resources which will serve as guidebook for teaching mathematics in STEM context for STEM students. The guidebook also contain appropriate lesson plans

Some results on the digamma function

The digamma function is defined for $x\u3e0$ as a locally summable function on the real line by $$\psi(x)=-\gamma+\int_0^{\infty}\frac{e^{-t}-e^{-xt}}{1-e^{-t}}\,dt\,.$$ In this paper we use the neutrix calculus to extend the definition for digamma function for the negative integers. Also we consider the derivatives of the digamma function for negative integers

Results on the Colombeau products of the distribution x_+^−r−1/2 with the distributions x_-^−k−1/2 and x_-^k−1/2

Results on the products of the distribution x_+^−r−1/2 with the distributions x_-^−k−1/2 and x_-^k−1/2 are obtained in the differential algebra G(R) of Colombeau generalized functions, which contains the space D'(R) of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in G(R). This enables treating the results in terms of distributions again