Nalvaizmiku: Import words via API

2026-01-13T15:50:36Z

Import words via API

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==== valsi ====
ne'o'o
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Sat Nov 12 19:28:41 2022

== English ==
=== Definition #73027 - Preferred ===

==== selma'o ====
VUhU3
==== definition ====

mekso quaternary operator – Pochhammer symbol: with/for input MATH
$(X_1, X_2, X_3, X_4)$

(X1, X2, X3, X4), this word/function outputs MATH
$\prod_{k = 0}^{X_2 - 1} (X_1 + (-1)^{(1 - X_3)} X_4 k)$

<img alt="$\prod_{{k = 0}}^{{X_2 - 1}}$" src="/jbovlaste_export/Lex33EzVzz/img1.png" style="height: 3.01ex; vertical-align: -0.81ex; "/>(X1 + (- 1)(1-X3)X4k); by default, X4 = 1 unless explicitly defined otherwise.

==== notes ====

For the basic definition, all inputs (especially those which are not X1) should be nonnegative integers; X3 can be further restricted to 0 (for the falling factorial) and 1 (for the rising factorial); X4 > 0 will be typical. X2 < 1 yields the empty product, which is typically defined by convention to be 1, regardless of all other inputs (so long as they are valid/belong to the domain). X2 is the number of terms in the aforementioned defining product and interacts with X4 in somewhat-complicated ways; be careful to avoid multiplying by nonpositive numbers unless such is actually desired (which may break certain recursive formulas); in order to avoid negative terms, enforce that X2 < 1 + min(Set MATH
$(1, X_1 \% X_4)) + ((X_1 - (X_1 \% X_4))/X_4)$

(1, X1%X4)) + ((X1 - (X1%X4))/X4), where: "%" denotes the modulus/remainder (see: "[[vei'u|vei'u]]") of its left-hand/first input (here: X1) wrt/when integer-dividing it by its right-hand/second input (here: X4); recall: x%y in [0, y) for all real numbers x and y : y > 0. Also, X4 = 1 by default. See also: "[[ne'o|ne'o]]", "[[ne'oi|ne'oi]]".

==== gloss words ====

<ul><li>[[natlang/en/ascending factorial|ascending factorial]]</li><li>[[natlang/en/ascending sequential product|ascending sequential product]]</li><li>[[natlang/en/descending factorial|descending factorial]]</li><li>[[natlang/en/descending sequential product|descending sequential product]]</li><li>[[natlang/en/factorial power|factorial power]]</li><li>[[natlang/en/falling factorial|falling factorial]]</li><li>[[natlang/en/falling sequential product|falling sequential product]]</li><li>[[natlang/en/lower factorial|lower factorial]]</li><li>[[natlang/en/partial factorial|partial factorial]]</li><li>[[natlang/en/partial n-tuple factorial|partial n-tuple factorial]]</li><li>[[natlang/en/Pochhammer|Pochhammer]]</li><li>[[natlang/en/Pochhammer factorial|Pochhammer factorial]]</li><li>[[natlang/en/Pochhammer function|Pochhammer function]]</li><li>[[natlang/en/Pochhammer polynomial|Pochhammer polynomial]]</li><li>[[natlang/en/Pochhammer symbol|Pochhammer symbol]]</li><li>[[natlang/en/rising factorial|rising factorial]]</li><li>[[natlang/en/rising sequential product|rising sequential product]]</li><li>[[natlang/en/upper factorial|upper factorial]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1

==== time ====
Sat Nov 12 21:21:43 2022

 Examples
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=== Etymology ===

ne'o'o - Revision history

Nalvaizmiku: Import words via API