zei'i'au VUhU3 experimental cmavo

unary mekso operator: (analytically continued) Riemann zeta function zeta(z), for complex-valued input z.

On grammatical class:

cu'a
unary mathematical operator: absolute value/norm |a|.
de'o
binary mathematical operator: logarithm; [log/ln a to base b]; default base 10 or e.
fe'a
binary mathematical operator: nth root of; inverse power [a to the 1/b power].
gei'au
mekso 7-ary operator: for input (X1 = z, X2 = (ai)= (bj)= p, X5 = q, X6 = h1, X= h2), this word/function outputs/yields \sumn=0^\infty (((\prodi = 1p (ne'o'o(ai,n,1,h= 1q (ne'o'o(bj,n,1,h; by default, X6 = 1 = X7 unless explicitly specified otherwise.
ne'o
unary mathematical operator: factorial; a!.
ne'o'a
mekso ternary operator: the generalized incomplete (factorial-extending) Pi function; for input (X1, X this word outputs the definite integral of t^X1 e^-t with respect to t from X2 to X3 (see notes for default values).
ne'o'au
mekso quaternary operator: polygamma function; for input X1, X, outputs the (-X2)th derivative of Log(ne'o'a(X1, X)) with respect to X1.
ne'o'o
mekso quaternary operator – Pochhammer symbol: with/for input (X1, X, this word/function outputs \prodk = 0^X2 - 1 (X; by default, X4 = 1 unless explicitly defined otherwise.
pau'au
ternary mekso operator: p-adic valuation; outputs (positive) infinity if x1 = 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x3)x divides x1)), where pn is the nth prime (such that p1 = 2).
po'i'ei
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).
pu'e'ei
mekso binary operator: generate span; outputs span(X1, X= spanX; set of all (finite) sums of terms of form c v, where v is an element of algebraic structure X1 (wherein scalar multiplication and summation is defined), and c is a scalar belonging to ring X2.
tai'i'au
8-ary mekso operator: the X1th nonnegative sum of X2 mutually-distinct perfect X3th-powers (i.e.: of integers) in X4 mutually truly-distinct ways, requiring exactly X5 terms to be negative in each sum (counting with(out^X6) multiplicity), requiring exactly X7 terms to be repeated between sums (counting with(out^X8) multiplicity), according to the usual ordering of the integers.
va'a
unary mathematical operator: additive inverse; [- a].
vei'o
binary mekso operator: form quotient space X1/X.
bai'ei (exp!)
unary mathematical operator: successor/augment/increment (by one), succ(a) = a++ = a+1
cu'ai (exp!)
binary mathematical operator: vector norm/magnitude of vector a in structure (normed vector space) b.
de'au'u (exp!)
mekso ternary operator: positive super-logarithm; the super-logarithm (inverse operator of hyper-operator with respect to "height" of power tower) of a with base b and of order c-2.
fe'au'u (exp!)
mekso ternary operator: positive super-root; the bth super-root (inverse operator of hyper-operator with respect to base) of a of order c-2.
fei'i (exp!)
mekso variable-arity (at most ternary) operator: number of prime divisors of number X1, counting with or without multiplicity according to the value X2 (1 xor 0 respectively; see note for equality to -1 and for default value), in structure X3.
jau'au (exp!)
unary mathematical operator: length/number of components/terms of/in object/array/formal string/sequence/word/text in some alphabet/base/basis which includes each digit; number of digits/components/entries
ka'au (exp!)
mekso unary operator: cardinality (#, | |)
ne'oi (exp!)
unary operator: primorial a#
pau'oi (exp!)
unary mathematical operator: predecessor/diminish/decrement (by one), \operatornamepred(a) = a-- = a-1
pi'ei'oi (exp!)
mathematical ternary operator: prime-generating function.
zei'i'au (exp!)
unary mekso operator: (analytically continued) Riemann zeta function zeta(z), for complex-valued input z.

In notes:

ma'oi'e (exp!)
Like "ma'oi" but outputs the officially-designated/canonical sub-selma'o (if any) to which the immediately following and quoted word (cmavo) belongs, otherwise outputting the whole relevant selma'o in fashion equivalent to "ma'oi".