Infinite Series Explorer
Mathematica can explicitly evaluate a large number of infinite power series. This Demonstration gives some elementary examples with simple coefficients that sum to exponential, trigonometric, hyperbolic, and logarithmic functions. Not included are hypergeometric functions, binomial expansions, inverse trigonometric functions, or Dirichlet series such as the Riemann zeta function.
Snapshot 1: expansions of Bessel functions of zero order can be represented; higher orders would require coefficients such as
Snapshot 2: the expansion for the inverse tangent can be obtained; for , this gives the Leibniz-Gregory series
Snapshot 3: for , this gives the series
Snapshot 4: the simplest geometric series, convergent for