Definition:Sequence/Doubly Subscripted
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Definition
A doubly subscripted sequence is a mapping whose domain is a subset of the cartesian product $\N \times \N$ of the set of natural numbers $\N$ with itself.
It can be seen that a doubly subscripted sequence is an instance of a family of elements indexed by $\N^2$.
A doubly subscripted sequence can be denoted $\left\langle{a_{m n} }\right\rangle_{m, \, n \mathop \ge 0}$
Also see
- Results about sequences can be found here.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.9$: Generating Functions: Exercise $12$