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InverseSeries

Computes the reversion of a power series: given the series for y = f(x) with f(0) = 0 and f'(0) != 0, returns the series for the inverse x = f^(-1)(y).

$ wo 'InverseSeries[Series[Sin[x], {x, 0, 5}]]'
SeriesData[x, 0, {1, 0, 1/6, 0, 3/40}, 1, 6, 1]

$ wo 'InverseSeries[Series[Exp[x] - 1, {x, 0, 4}]]'
SeriesData[x, 0, {1, -1/2, 1/3, -1/4}, 1, 5, 1]

$ wo 'InverseSeries[Series[Tan[x], {x, 0, 6}]]'
SeriesData[x, 0, {1, 0, -1/3, 0, 1/5}, 1, 7, 1]

$ wo 'InverseSeries[Series[x + x^2, {x, 0, 5}]]'
SeriesData[x, 0, {1, -1, 2, -5, 14}, 1, 6, 1]

$ wo 'InverseSeries[Series[Sin[x], {x, 0, 5}], y]'
SeriesData[y, 0, {1, 0, 1/6, 0, 3/40}, 1, 6, 1]

$ wo 'Normal[InverseSeries[Series[Sin[x], {x, 0, 5}]]]'
x + x^3/6 + (3*x^5)/40