Category:Summations
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This category contains results about Summations.
Definitions specific to this category can be found in Definitions/Summations.
Let $\map R j$ be a propositional function of $j$.
Then we can write the summation as:
- $\ds \sum_{\map R j} a_j = \text{ The sum of all $a_j$ such that $\map R j$ holds}$.
If more than one propositional function is written under the summation sign, they must all hold.
Subcategories
This category has the following 14 subcategories, out of 14 total.
Pages in category "Summations"
The following 91 pages are in this category, out of 91 total.
C
E
- Exchange of Order of Indexed Summations
- Exchange of Order of Indexed Summations over Rectangular Domain
- Exchange of Order of Indexed Summations/Rectangular Domain
- Exchange of Order of Summation
- Exchange of Order of Summation with Dependency on Both Indices
- Exchange of Order of Summation with Dependency on Both Indices/Example
- Exchange of Order of Summation with Dependency on Both Indices/Infinite Series
- Exchange of Order of Summation with Dependency on Both Indices/Proof
- Exchange of Order of Summation/Example
- Exchange of Order of Summation/Finite and Infinite Series
- Exchange of Order of Summation/Infinite Series
- Exchange of Order of Summations over Finite Sets
- Exchange of Order of Summations over Finite Sets/Cartesian Product
- Exchange of Order of Summations over Finite Sets/Subset of Cartesian Product
G
I
- Indexed Summation does not Change under Permutation
- Indexed Summation of Multiple of Mapping
- Indexed Summation of Sum of Mappings
- Indexed Summation of Zero
- Indexed Summation over Adjacent Intervals
- Indexed Summation over Interval of Length One
- Indexed Summation over Interval of Length Two
- Indexed Summation over Translated Interval
- Indexed Summation without First Term
P
S
- Sum of Elements in Inverse of Cauchy Matrix
- Sum of Sequence as Summation of Difference of Adjacent Terms
- Sum of Summations equals Summation of Sum
- Sum of Summations equals Summation of Sum/Infinite Sequence
- Sum of Summations equals Summation of Sum/Infinite Sequence/Proof 1
- Sum of Summations equals Summation of Sum/Infinite Sequence/Proof 2
- Sum of Summations over Overlapping Domains
- Sum of Summations over Overlapping Domains/Infinite Series
- Sum of Zero over Finite Set
- Sum over Complement of Finite Set
- Sum over Disjoint Union of Finite Sets
- Sum over j of Function of Floor of mj over n
- Sum over j of Function of Floor of mj over n/Corollary
- Sum over k of Floor of Log base b of k
- Sum over k of Floor of Root k
- Sum over k of Sum over j of Floor of n + jb^k over b^k+1
- Sum over k of Sum over j of Floor of n + jb^k over b^k+1/Corollary
- Sum over Union of Finite Sets
- Summation by k of Product by r of x plus k minus r over Product by r less k of k minus r
- Summation of General Logarithms
- Summation of i from 1 to n of Summation of j from 1 to i
- Summation of Multiple of Mapping on Finite Set
- Summation of Powers over Product of Differences
- Summation of Powers over Product of Differences/Example
- Summation of Product of Differences
- Summation of Products of n Numbers taken m at a time with Repetitions
- Summation of Sum of Mappings on Finite Set
- Summation of Summation over Divisors of Function of Two Variables
- Summation of Unity over Elements
- Summation of Zero
- Summation of Zero/Finite Set
- Summation of Zero/Indexed Summation
- Summation of Zero/Set
- Summation over Cartesian Product as Double Summation
- Summation over Finite Set Equals Summation over Support
- Summation over Finite Set is Well-Defined
- Summation over Interval equals Indexed Summation
- Summation over k of Ceiling of k over 2
- Summation over k of Ceiling of mk+x over n
- Summation over k of Floor of k over 2
- Summation over k of Floor of mk+x over n
- Summation over k of Floor of x plus k over y