Nested derivatives: a simple method for computing series expansions of inverse functions
Copyright policy )Nested derivatives: a simple method for computing series expansions of inverse functions
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first N terms of the series. We show several examples of its application in calculating the inverses of some special functions.
- State University of New York at Potsdam United States
- State University of New York at New Paltz United States
30B10 (Primary) 30D10, 33E20 (Secondary), Mathematics - Classical Analysis and ODEs, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Software, source code, etc. for problems pertaining to sequences, series, summability, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Mathematics
30B10 (Primary) 30D10, 33E20 (Secondary), Mathematics - Classical Analysis and ODEs, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Software, source code, etc. for problems pertaining to sequences, series, summability, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Mathematics
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