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# Series

In mathematics, a series is an (often infinite) sum of terms specified by some rule.

Series is a middle school-level concept. It is an Advanced Placement Calculus BC topic and is listed in the California State Standards for Calculus.

### Examples

 Arithmetic Series: An arithmetic series is a series in which the difference between any two consecutive terms is a constant. Bessel Function of the First Kind: A Bessel function of the first kind is a solution to a particular nonlinear second-order differential equation. Bessel functions appear in many physics applications when solving classical partial differential equations in cylindrical coordinates. Geometric Series: A geometric series is a series in which the ratio of any two consecutive terms is always the same. Power Series: A power series is a sum of powers of a variable. A power series is essentially an infinite polynomial. Riemann Zeta Function: The Riemann zeta function is a special function of mathematics and physics that is intimately related to deep results surrounding the prime number theorem. Taylor Series: A Taylor series is a power series of a function around a given point.