Formal calculus MOC

Formal derivative

Let 𝑉 be a vector space (or, in particular, a field) and 𝑉{𝑧} denote formal sums over 𝑉. The formal derivative fcalc

𝑑𝑑𝑧:𝑉{𝑧}→𝑉{𝑧}

is defined by extending the rules

𝑑𝑑𝑧(𝑧𝑛)={0𝑛=0𝑛𝑧𝑛−1𝑛≠0

by linearity. The formal derivative therefore constitutes a derivation on the algebra of Laurent polynomials 𝕂[𝑧,𝑧−1].

See also

• Degree operator on formal sums over a vector space

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