In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, "m"th "g -…