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A mathematic operator acting on a given space of sequences
In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space). Sequence transformations include linear mappings such as convolution with another sequence, and resummation of a sequence and, more generally, are commonly used for series acceleration, that is, for improving the rate of convergence of a slowly convergent sequence or series. Sequence transformations are also commonly used to compute the antilimit of a divergent series numerically, and are used in conjunction with extrapolation methods.

Classical examples for sequence transformations include the binomial transform, Möbius transform, Stirling transform and others.

Simplest examples of (linear) sequence transformations include shifting all elements, (resp. = 0 if n + k < 0) for a fixed k, and scalar multiplication of the sequence. A less trivial example would be the discrete convolution with a fixed sequence. A particularly basic form is the difference operator, which is convolution with the sequence and is a discrete analog of the derivative. The binomial transform is another linear transformation of a still more general type. An example of a nonlinear sequence transformation is Aitken's delta squared process, used to improve the rate of convergence of a slowly convergent sequence. An extended form of this is the Shanks transformation. The Möbius transform is also a nonlinear transformation, only possible for integer sequences.