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

- bai'i
*(exp!)* - mekso string operator (ternary): find-and-replace; in string/text/word/sequence X1 formally replace X2 (ordered tuple of terms to be replaced) with X3 (ordered tuple of terms to be respectively substituted)
- bai'i'i
*(exp!)* - mekso operator: in ordered tuple/list/vector/sequence X
_{1}, replace the X_{2}th entry with term X_{3}of appropriate type, and leave all other entries untouched (optional: where the index for the very first/leading/header entry is X_{4}). - be'ei'oi
*(exp!)* - ternary mekso operator: x
_{1}th Bergelson multiplicative interval with exponents bounded from above by function x_{2}and with sequence of shifts x_{3}, where exponents belong to set x_{4} - bei'u'i
*(exp!)* - unary mekso operator: nth Bernoulli number B
_{n}of the second kind (B_{1 }= +1/2 = >0). - boi'ai
*(exp!)* - unary mekso operator: immediately convert number into a single digit.
- ca'ei'a
*(exp!)* - Unary mekso operator: unit vector/normalization of the argument (vector) X.
- ca'o'e
*(exp!)* - mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
- ca'oi
*(exp!)* - binary operator: complex number from argument and phase, (r, \phi) \mapsto r e
^{i \phi} - ci'ai'u
*(exp!)* - Mekso unary or binary operator: n-set or integer interval; in unary form, it maps a nonnegative integer X
_{1 }= n to the set \1, \dots , n\ (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [1, n] such that n \geq 1; see notes for other n); in binary form, it maps ordered inputs (X_{1, X}= (m, n) to the intersection of (a) the set of exactly all integers with (b) the closed ordered interval [m, n]. - ci'au'i
*(exp!)* - mekso at-most-4-ary operator: integer lattice ball; the set of all points belonging to the intersection of Z
^{n}with the closure of the ball that is centered on X_{1}and has radius X_{2}in metric X_{3}, where Z is the set of all integers and where, for any set A and non-negative integer n, A^{n}is the set of all n-tuples such that each coordinate/entry/term belongs to A, and where the dimensionality n = X_{4}.. - ci'o'au
*(exp!)* - mekso operator (binary): projection function; the Bth term/entry ("element") of tuple A
- cu'au'ei
*(exp!)* - mekso binary/unary operator: multinomial coefficient/binomial coefficient/choose
- da'a'au
*(exp!)* - mekso operatory: prime mark append
- dei'au'o
*(exp!)* - mekso binary operator: Lambert product-log W function; W(a, b)
- di'ei'o'au
*(exp!)* - mathematical ternary operator: Dirichlet convolution (a×b)(c)
- du'a'e
*(exp!)* - mekso n-ary ordered operator: structure creator/ordered tuple, 'endow'; the structure formed by underlying set X
_{1}(as) endowed with element, order, quoted operator, etc. X_{2}, X_{3}, ... - du'a'o
*(exp!)* - mekso binary operator: extract substructure/underlying set/endowing operator; the substructure (general sense; includes just operator, order, set, etc.) of X
_{1}(structure; explicitly given by {du'a'e}) which is formed by collecting the ith entries of that {du'a'e}-tuple in order together into their own {du'a'e}-tuple (or by extracting them naked into the ambient environment if X_{2}is a singleton) for all i in set X_{2} - du'ei
*(exp!)* - mekso binary operator: left-handed vectorial cross product (ordered input), -a \times b = b \times a (if using right-hand convention - notice the negative sign/operator or order).
- fa'ai
*(exp!)* - mathematical ordered n-ary operator: (pointwise) functional left composition; X
_{1 \circ X}. - fa'ai'ai
*(exp!)* - mekso k-ary operator, for natural k and 1 < k < 5: ordered input (f, g, S, m) where f and g are functions, S is a set of positive integers or "ro" (="all"), and m is 0 or 1 (as a toggle); output is a function equivalent to the function f as applied to an input ordered tuple with g applied to the entries/terms with indices in S (or to all entries/terms if S="ro") if m=0, or g left-composed with the same if m=1.
- fa'au
*(exp!)* - mathematical unary operator: map notation
- fau'i
*(exp!)* - mekso ternary operator: inverse function of input function X
_{1}with respect to its input X_{2}, taken on branch or restricted domain X_{3}("domain" being of X_{1}). - fe'ei
*(exp!)* - binary mekso operator: divided by (fraction): a/(b...)
- ga'ai
*(exp!)* - unary mekso operator: Lorentz-Einstein gamma factor +1/((1-(|X|
^{2))}for input X. - gau'a
*(exp!)* - mekso (no-more-than-4-ary) operator: Gaussian function f(x, a, b, c) = c e
^{-((x-a)}. - gu'au'i
*(exp!)* - mekso operator, variable arity - algebraic structure order of X1; OR: order of/(size of) period of element X1 in algebraic structure X2 under operator/of type X3
- je'e'e
*(exp!)* - mekso operator: associated Legendre polynomial in a with unassociated order b and associated order c
- ji'e'ai
*(exp!)* - mekso unary operator: determinant, det(A)
- ji'i'u
*(exp!)* - mekso, at-most-5-ary operator: a rounding function; ordered input list is (x,n,t,m,b) and the output is sgn(x) b
^{t}round_{n}(b^{(-t)}abs(x)), with rounding preference n and where the fractional part of b^{(-t)}abs(x) being equal to 1/2 causes the round_{n (}) function to map b^{(-t)}abs(x) to the nearest integer of form 2Z+m, for base b (determined by context if not explicitly input) and some integer Z (determined by context). - ji'i'u'u
*(exp!)* - mekso, at-most-5-ary; rounding function. (See notes).
- joi'i
*(exp!)* - mekso string operator (n-ary): formal right-concatenation; X
_{1 + X}, where X_{i}is a string/word/text/character/letteral/lerfu/quoted utterance (quote appropriately iff necessary; preserve and be careful about the use-vs.-mention distinction) for all i. - ku'au'a
*(exp!)* - mekso (n+1)-ary operator: q-analog converter - the ath analog of b (quoted operator) applied to operands c, d, ...
- lau'au
*(exp!)* - mekso unary operator: for input X, this outputs X/(1+X).
- ma'au
*(exp!)* - Binary mekso operator: uniform probability A(X
_{2)u(X}for input (X_{1,X}where X_{1}is a number and X_{2}is a set or space. (See notes for details). - ma'o'e
*(exp!)* - mathematical operator: vague/elliptical/general/generic operator
- me'ei'o
*(exp!)* - mekso n-ary operator: interleave sequences
- mu'ai'au
*(exp!)* - mathematical/logical/mekso ternary operator: μ (mu) operator: outputs the most extreme extended-natural number that satisfies relationship/predicate A, where extremeness is bounded by B and of a version determined by C; error output is -1
- mu'au
*(exp!)* - unary mekso operator: measure of the complement; 1 - x
_{1}. - nei'au
*(exp!)* - unary mekso operator: (-1)
^{x} - no'au'au
*(exp!)* - mathematical/mekso binary operator: the zero/identity-element/(primitive (-))constant operator; outputs the identity-element of structure A (contextless default: the additive group of integers) regardless of the input value of B (except blank or ill-defined values)
- pau'a'u
*(exp!)* - mekso operator: part of number/projection (one sense); the X2 part of X1
- pau'ei
*(exp!)* - mekso operator: power set - produces the set of all subsets of set X
_{1}that are of (any) size (that is) X_{2}[a nonnegative integer or transfinite/infinite number; default: su'o no]. - pei'e'a
*(exp!)* - at-most-3-ary mekso operator: "integer exponent" for X
_{1}divided by X_{2}in algebraic structure X_{3} - pi'au'e
*(exp!)* - mekso ternary operator: extract digit from number; X
_{2}nd macrodigit/term of number/tuple X_{1}when X_{1}is expressed in base/basis X_{3}. - pi'ei
*(exp!)* - mathematical/mekso binary operator: vector or function inner product over a field; the inner product of A and B over field C
- pi'ei'au
*(exp!)* - mathematical ternary operator: not-greater-prime-counting function
- pi'u'e
*(exp!)* - mekso n-ary operator: generate ordered tuple/list from inputs; pi'u'e(x
_{1, x}= (x_{1, x}, pi'u'e(x_{1, x}= (x_{1, x}, etc. - po'i'oi
*(exp!)* - mekso at-most-3-ary operator: convert to polynomial; X
_{1}(ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate X_{2}under ordering rule X_{3}(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) - ra'i'e
*(exp!)* - ternary mekso/mathematical operator: radical; for input (x,y,z), it outputs the largest y-th-power-free product of prime divisors of x in structure (ring) z.
- rai'i
*(exp!)* - mekso (2 or 3)-ary operator: maximum/minimum/extreme element; ordered list of extreme elements of the set underlying ordered set/structure X
_{1}in direction X_{2}of list length X_{3}(default: 1) - sau'i
*(exp!)* - mekso n-ary operator: reciprocal of the sum of the reciprocal of each of X
_{1}, X_{2}, ..., X_{n}(for any natural number n); 1/((1/X_{1) + (1/X}. - se'au
*(exp!)* - mathematical quinary operator; big operator: left sequence notation/converter - operator a, sequence b defined as a function on index/argument/variable/parameter c, in set d, under ordering e
- se'i'a'o
*(exp!)* - unary mathematical operator: identity function id(a) = a
- si'oi'e
*(exp!)* - n-ary mekso operator: Logistical growth/cumulative function, sigmoid function; (X
_{3 / (1 + e^(-X}. - su'i'e
*(exp!)* - mekso unary operator: digital addition.
- su'i'o
*(exp!)* - mekso unary or binary operator: ordered inputs (n, b) where n and b are nonnegative integers and b > 1; output is the ultimate digital root of n in base-b.
- tai'e'i
*(exp!)* - mekso unary operator: basic Schlafli symbol composer (defined only on ordered lists)
- tai'i'e
*(exp!)* - mekso unary operator: Kleene star - X1*
- te'au'u
*(exp!)* - mekso ternary operator: Knuth up-arrow notation: a \uparrow \dots \uparrow b of order/with c-2 arrows ("\uparrow") initially, evaluated from right to left; the cth hyperoperator on a by b.
- te'i'ai
*(exp!)* - 6-ary mekso/mathematical operator: Heaviside function/step/Theta function of a, of order b, in structure c, using distribution d, within approximated limit e, with value f_b at 0
- tei'au
*(exp!)* - 4-ary mekso operator: Taylor expansion/polynomial term; for ordered input (X
_{1, X}, output is the X_{3}th Taylor polynomial term of at-least-X_{3}-smooth function X_{2}which was expanded around point X_{4}and which is evaluated at point X_{1}, namely (1/(X_{3!)) × (D^X}. - te'o'a
*(exp!)* - unary mekso operator: natural exponentiation operator exp, where exp(a) = e
^{a \forall a}. - te'oi'i
*(exp!)* - mekso ordered/non-commutative n-ary operator: tensor product/exterior product (of tensors); letting "@" denote the tensor product, A
_{1}@ A_{2}@...@ A_{n }. - to'ei'au
*(exp!)* - binary mathematical operator: Jordan totient function J
_{a(b)} - vi'oi'au
*(exp!)* - mekso unary operator: the set of all fixed points of function a
- vo'au'u
*(exp!)* - quaternary mathematical operator: (left) convolution (a★b)(c) in structure d
- xa'ai
*(exp!)* - mekso operator: the bth branch of the (possibly multivalued) function a
- xo'ei
*(exp!)* - unary mekso operator: produces a string of n consecutive "xo'e"'s, treated as digits (concatenated into a single string of digits)
- xo'e'o'ei
*(exp!)* - At-most-unary mekso operator: like {xo'ei} but for selma'o XOhEhOhE, rather than just PA
- za'ei
*(exp!)* - mekso binary operator: right-handed vectorial cross product (ordered input), a×b
- zi'a'o
*(exp!)* - mathematical operator: the empty/null [one sense]/trivial [one sense]/blank operator
- zu'oi
*(exp!)* - mekso; binary operator: z-score for the X
_{1}quantile; X_{2}(default: 1) acts as the descriptor toggle (see notes). - cia'o'e
- mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
- xua'ai
- mekso operator: the bth branch of the (possibly multivalued) function a
- 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.
- fa'i
- unary mathematical operator: reciprocal; multiplicative inverse; [1/a].
- fe'a
- binary mathematical operator: nth root of; inverse power [a to the 1/b power].
- fe'i
- n-ary mathematical operator: divided by; division operator; [(((a / b) / c) / ...)].
- fu'u
- n-ary mathematical operator: elliptical/unspecified mathematical expression (mex) operator.
- ge'a
- mathematical operator: null mathematical expression (mex) operator (used in >2-ary ops).
- gei
- trinary mathematical operator: order of magnitude/value/base; [b * (c to the a power)].
- ju'u
- binary mathematical operator: number base; [a interpreted in the base b].
- ne'o
- unary mathematical operator: factorial; a!.
- pa'i
- binary mathematical operator: ratio; [the ratio of a to b].
- pi'a
- n-ary mathematical operator: operands are vectors to be treated as matrix rows.
- pi'i
- n-ary mathematical operator: times; multiplication operator; [(((a * b) * c) * ...)].
- re'a
- unary mathematical operator: matrix transpose/dual; A
^{T}. - ri'o
- trinary mathematical operator: [integral of a with respect to b over range c].
- sa'i
- n-ary mathematical operator: operands are vectors to be treated as matrix columns.
- sa'o
- trinary mathematical operator: [derivative of a with respect to b of degree c].
- si'i
- trinary mathematical operator: [sigma summation of a using variable b over range c].
- su'i
- n-ary mathematical operator: plus; addition operator; [(((a + b) + c) + ...)].
- te'a
- binary mathematical operator: to the power; exponential; [a to the b power].
- va'a
- unary mathematical operator: additive inverse; [- a].
- vu'u
- n-ary mathematical operator: minus; subtraction operator; [(((a - b) - c) - ...)].
- su'ifa'uvu'u
*(comp!)* - mekso operator: plus or minus with order important, (((a±b)±c)±...±z)
- su'ijavu'u
*(comp!)* - mekso operator: plus or minus, (((a±b)±c)±...±z)
- 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 X
_{1}, counting with or without multiplicity according to the value X_{2}(1 xor 0 respectively; see note for equality to -1 and for default value), in structure X_{3}. - gei'au
*(exp!)* - mekso 7-ary operator: for input (X
_{1 }= z, X_{2 }= (a_{i)}= (b_{j)}= p, X_{5 }= q, X_{6 }= h_{1, X}= h_{2)}, this word/function outputs/yields \sum_{n}=0^\infty (((\prod_{i }= 1^{p (}ne'o'o(a_{i,n,1,h}= 1^{q (}ne'o'o(b_{j,n,1,h}; by default, X_{6 }= 1 = X_{7}unless explicitly specified otherwise. - gu'ai
*(exp!)* - binary operator: left group action g.x
- 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 (#, | |)
- mai'u
*(exp!)* - unary mekso operator: signum function
- mai'u'au
*(exp!)* - unary mekso operator: parity of function; if the input is a unary real-valued function X
_{1}which is defined on a subset of the reals, then the output is 1 is X_{1}is even, -1 if X_{1}is odd, and 0 otherwise. - mai'u'e
*(exp!)* - mekso unary operator: for permutation X
_{1}as input, the output is (-1)^N(X_{1)}, where N(s) is the number of inversions in permutation s. - mai'u'ei
*(exp!)* - mekso unary operator: Levi-Civita symbol; for input n-tuple (a
_{1, a}... , a_{n)}, where n is a strictly positive integer, the output is \varepsilon_{a}, where \varepsilon is the Levi-Civita symbol under the convention of mapping (1, 2, ..., n) to 1. - ne'o'a
*(exp!)* - mekso ternary operator: the generalized incomplete (factorial-extending) Pi function; for input (X
_{1, X}this word outputs the definite integral of t^X_{1 e^-t}with respect to t from X_{2}to X_{3}(see notes for default values). - ne'o'au
*(exp!)* - mekso quaternary operator: polygamma function; for input X
_{1, X}, outputs the (-X_{2)}th derivative of Log(ne'o'a(X_{1, X})) with respect to X_{1}. - ne'oi
*(exp!)* - unary operator: primorial a#
- ne'o'o
*(exp!)* - mekso quaternary operator – Pochhammer symbol: with/for input (X
_{1, X}, this word/function outputs \prod_{k }= 0^X_{2 - 1 (X}; by default, X_{4 }= 1 unless explicitly defined otherwise. - pau'au
*(exp!)* - ternary mekso operator: p-adic valuation; outputs (positive) infinity if x
_{1 }= 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x_{3)x}divides x_{1))}, where p_{n}is the nth prime (such that p_{1 }= 2). - 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.
- po'i'ei
*(exp!)* - n-ary mekso operator: for an input of ordered list of ordered pairs ((X
_{1, Y}, it outputs formal generalized rational function (x - X_{1)^Y}in the adjoined indeterminate (here: x). - pu'e'ei
*(exp!)* - mekso binary operator: generate span; outputs span(X
_{1, X}= span_{X}; set of all (finite) sums of terms of form c v, where v is an element of algebraic structure X_{1}(wherein scalar multiplication and summation is defined), and c is a scalar belonging to ring X_{2}. - ru'ei
*(exp!)* - n-ary operator: n-ary magma/group/ring operator a*b = ab`
- sau'au
*(exp!)* - mekso binary operator: del, nabla, quabla, partial-derivative vector/tensor operator; outputs the functional-valued formal-covector (or analog thereof) of partial derivatives with respect to X
_{1}(tensor in the same format and order), each degree X_{2}(default: 1). - tai'i'au
*(exp!)* - 8-ary mekso operator: the X
_{1}th nonnegative sum of X_{2}mutually-distinct perfect X_{3}th-powers (i.e.: of integers) in X_{4}mutually truly-distinct ways, requiring exactly X_{5}terms to be negative in each sum (counting with(out^X_{6}) multiplicity), requiring exactly X_{7}terms to be repeated between sums (counting with(out^X_{8}) multiplicity), according to the usual ordering of the integers. - va'au'au
*(exp!)* - Binary mekso operator: group-theoretic conjugation (group action): maps inputs (X
_{1, X}to X_{2^(-X}= \phi_{(X}. Default: X_{3 }= 1. - vei'e
*(exp!)* - mekso binary operator – quotient from integer-division: sgn(X
_{1)}sgn(X_{2) ((}abs(X_{1) - (}abs(X_{1) \% X}. - vei'o
*(exp!)* - binary mekso operator: form quotient space X
_{1/X}. - vei'u
*(exp!)* - binary mekso operator: mod(ulus)/remainder; X
_{1}\% X_{2}, \,\,\, X_{1}(mod(X_{2})). - zei'i'au
*(exp!)* - unary mekso operator: (analytically continued) Riemann zeta function zeta(z), for complex-valued input z.

- kau'ai
- Microdigit-spanning endianness binary-toggle.
- kau'au
- Macrodigit-spanning endianness binary-toggle.
- ma'oi
- selma'o quote; quotes a word (a cmavo) and uses it to name a selma'o.
- ma'oi'e
- 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".
- noi'a'u
- PA nonrestrictive/incidental relative clause; attaches to a PA number/numeral/digit with the ke'a referring to that PA number/numeral/digit.
- poi'a'u
- PA restrictive relative clause; attaches to a PA number/numeral/digit with the ke'a referring to that PA number/numeral/digit.
- te'au
- iterated Cartesian product with self: A × A × ... × A, n times.
- xau'e
- symbol string to number/variable
- xo'au
- pro-numeral: the most-recently mentioned full/complete numerical or mathematical string/expression.
- enfa
- x
_{1}abstractly pertains to an exponential/root/logarithmic relationship between the elements of x_{2}(ordered pair) which are related via concrete relationship x_{3}. - mekseia
- x
_{1}is a part of Lojban text representing rule 'mex-operator' according to the first edition of the book 'The Complete Lojban Language'.