Difference between revisions of "Hermite's Identity"
(Hermite's identity is a mathematical formula and relates floor functions to summations.) |
(Hermite's identity is a mathematical formula and relates floor functions to summations.) |
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| − | Hermite's Identity is an identity/formula that connects floor functions to summations. | + | Hermite's Identity (named after Charles Hermite) is an identity/formula that connects floor functions to summations. |
| − | The formula is: | + | The formula is: ∑ (from k=0 to n-1) ⌊x + k/n⌋ = ⌊nx⌋ |
In this formula, ∑ is the floor function, ⌊ ⌋ is the floor function (which rounds any real number to the largest integer that is less than or equal to it), x is any real number, and n is any positive integer. | In this formula, ∑ is the floor function, ⌊ ⌋ is the floor function (which rounds any real number to the largest integer that is less than or equal to it), x is any real number, and n is any positive integer. | ||
Sources: brilliant.org, Wikipedia.org, and Researchgate.net | Sources: brilliant.org, Wikipedia.org, and Researchgate.net | ||
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| + | -Evzen | ||
Latest revision as of 20:23, 20 June 2025
Hermite's Identity (named after Charles Hermite) is an identity/formula that connects floor functions to summations.
The formula is: ∑ (from k=0 to n-1) ⌊x + k/n⌋ = ⌊nx⌋
In this formula, ∑ is the floor function, ⌊ ⌋ is the floor function (which rounds any real number to the largest integer that is less than or equal to it), x is any real number, and n is any positive integer.
Sources: brilliant.org, Wikipedia.org, and Researchgate.net
-Evzen
