x_{1} is the generalized weighted Lehmer mean of data x_{2} (completely specified ordered multiset/list of numbers) of Lehmer order x_{3} (either a single extended-real number xor an ordered pair of two extended-real numbers) with weights x_{4} (completely specified ordered multiset/list of numbers with the same cardinality as x_{2}; defaults according to the Notes).

Possibly dimensionful. If the cardinality of x_{2} is n, then the cardinality of x_{4} is also n and, moreover, the weights default to 1/n each. If x_{3} is a single extended-real number p, then x_{3 }= (p, p-1) also. If x_{3 }= (p, q) validly for real p&q, then x_{1 }=Sum(w_{i y} in Set(1,...,n))/Sum(w_{i y} in Set(1,...,n)), where y_{i} is the ith term of x_{2} for all i, w_{i} is the ith term of x_{4} for all i, and n is the cardinality of x_{2} (and thus x_{4}). If x_{3} equals positive infinity (ma'uci'i), then the result x_{1} is the maximum of the data x_{2}; if x_{3} equals negative infinity (ni'uci'i), then the result x_{1} is the minimum of the data x_{2}.

- cnansari
- x
_{1}is the mean-value theorem mean/forward-difference-quotient mean of the elements of (multi)set x_{2}(1-element or 2-element set) under/for function x_{3}.