Infinite Series Explorer

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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.

Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA



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

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