Infinite Series

The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat, and Pascal. Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics.

Infinite Woodwinds is the second release in my line of next-gen virtual orchestral instruments. As with Infinite Brass, the goal was to create a collection of expressive virtual instruments that are easy to use and fun to play, allowing for quick results and realistic performances while sounding great out-of-the-box.

In a contemporary course in mathematical analysis, the concept of series arises as a natural generalization of the concept of a sum over finitely many elements, and the simplest properties of finite sums carry over to infinite series. Standing as an exception among these properties is the commutative law, for the sum of a series can change as a result of a rearrangement of its terms.