binomial series
The 'binomial series' is a fundamental concept in mathematics, extending the binomial theorem to any real or complex exponent.
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Definition
C1Mathematics
(technical, academic)An infinite series that expands a binomial expression raised to any real or complex power.
Example
- The expression (1 + x)^α can be expanded using the binomial series.
- Using the binomial series, we can approximate functions for small values of x.
C1Calculus
(technical)A power series that generalizes the binomial theorem, allowing the expansion of expressions like (1 + x)^α for any exponent.
Example
- In calculus, the binomial series is useful for finding the Taylor series of functions.
Similar
Terms that have similar or relatively close meanings to "binomial series":