ne'o'o

valsi

ne'o'o

type

experimental cmavo

creator

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="$\prod_Template:k = 0^Template:X 2 - 1$" 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") 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'oi".

gloss words

• ascending factorial
• ascending sequential product
• descending factorial
• descending sequential product
• factorial power
• falling factorial
• falling sequential product
• lower factorial
• partial factorial
• partial n-tuple factorial
• Pochhammer
• Pochhammer factorial
• Pochhammer function
• Pochhammer polynomial
• Pochhammer symbol
• rising factorial
• rising sequential product
• upper factorial

created by

krtisfranks

vote information

1

time

Sat Nov 12 21:21:43 2022

Examples

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