Taylor Series, Bernoulli Numbers, and the Tangent Function

A talk by Peter Schumer, Department of Mathematics, Middlebury College.

In calculus, students learn the Taylor series for several important functions such as the exponential, sine, and cosine functions. For these functions, the terms have an easily recognizable pattern. But what about other trigonometric functions? In particular, we’ll discuss the Taylor series for the tangent function which will lead naturally to an interesting set of numbers called the Bernoulli numbers. This talk should be a nice overview for those taking or wishing to review some calculus! All are welcome. Refreshments will be provided.