Multi-Index Notation

Definition: An n-dimensional multi-index is an n-tuple of natural numbers, of order Polynomials of several variables Given

Partial Differential Operators

Given a -times continuously differentiable function Example: For and We can define a notation for all differential operators with multi-index of a given order:

Examples:

• , gradient:
• , hessian:
• Higher orders denote tensors of mixed partials