Alternative form of lactoseries

(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.

A power series generalising Taylor series, in which the exponents may be positive or negative integers.

(mathematics, mathematical analysis) The divergent series whose terms are the reciprocals of the positive integers; the series ∑ₙ₌₁ ᪲1/n.

(electrical engineering) Of an electric motor, having the windings connected in series.

A television program which consists of several episodes that are broadcast at regular intervals. / A group of episodes of such a program.

(mathematics) Any series of the form 1/2A_o+ displaystyle ∑ₙ₌₁ ᪲(A_n cos nx+B_n sin nx).

(baseball, US) a cross-town playoff battle between the New York Mets and New York Yankees

(calculus) A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ.