(mathematics) A modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains the digit 9.

A model for nonlinear behavior similar to the Taylor series, differing in its ability to capture 'memory' effects.

(mathematics) A type of formal infinite series, a generalization of Puiseux series. They allow for arbitrary exponents of the indeterminate so long as the set supporting them forms a well-ordered subset of the value group.

Three lines of singly ionized helium found, usually in absorption, in the spectra of hot stars, produced by transitions of an electron with principal quantum number n=4 state from a higher energy level.

(Internet slang, humorous) The Internet.

plural of series finale

plural of series original

(mathematics) The Maclaurin series expansion of the function f(x) = (1 + x)^α, for arbitrary complex α; the series ∑ₖ₌₀ ᪲𝛼 choose kxᵏ, where 𝛼 choose k=(𝛼(𝛼-1)(𝛼-2)…(𝛼-k+1))/(k!).

(calculus) Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function f, the power series f(0)+(f'(0))/(1!)x+(f(0))/(2!)x²+(f'(0))/(3!)x³+⋯=∑ₙ₌₀ ᪲(f⁽ⁿ⁾(0))/(n!),xⁿ.

(mathematics) The divergent infinite series ∑ₙ₌₀ ᪲(-1)ⁿ=1-1+1-1+⋯.