po'i'ei VUhU3 experimental cmavo

n-ary mekso operator: for an input of ordered list of ordered pairs ((X1, Y, it outputs formal generalized rational function (x - X1)^Y in the adjoined indeterminate (here: x).

n may be infinite, under the condition that the function is well-defined. In the definition, adjacency of terms denotes multiplication in the relevant algebraic structure. If there is an i such that Yi is omitted, then Yi = 1 by default. For any i, there is no constraint on the values which may be taken by Xi or Yi. See also: "po'i'oi".

In notes:

po'i'oi (exp!)
mekso at-most-3-ary operator: convert to polynomial; X1 (ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate X2 under ordering rule X3 (default for finite list: the first entry is the coefficient of the highest-degree term and each subsequent entry is the next lesser-degree coefficient via counting by ones and wherein the last entry is the constant term)
x1 is a formal polynomial with coefficients x2 (ordered list) of degree x3 (li; nonnegative integer) over structure/ring x4 (to which coefficients x2 all belong) and in indeterminant x5.