Multi-index notationMulti-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices. An n-dimensional multi-index is an n-tuple of non-negative integers (i.e. an element of the n-dimensional set of natural numbers, denoted ). For multi-indices and one defines: Componentwise sum and difference Partial order Sum of components (absolute value) Factorial Binomial coefficient Multinomial coefficient where .
CorecursionIn computer science, corecursion is a type of operation that is to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data.
