Series Reversion

Series reversion is the computation of the Coefficients of the inverse function given those of the forward function.For a function expressed in a series as

(1)

(2)

	(3)

			(4)
			(5)
			(6)
			(7)
			(8)
			(9)
			(10)

	(11)

where

(12)

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 316-317, 1985.

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 297, 1987.

Dwight, H. B. Table of Integrals and Other Mathematical Data, 4th ed. New York: Macmillan, 1961.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 411-413, 1953.

• abc Conjecture
• Abelian
• Abelian Category
• Abelian Differential
• Abelian Function
• Abelian Group
• Abelian Integral
• Abelian Variety
• Abel's Curve Theorem
• Abel's Functional Equation
• Abel's Identity
• Abel's Impossibility Theorem
• Abel's Inequality
• Abel's Irreducibility Theorem
• Abel's Lemma
• Abel's Test
• Abel's Theorem
• Abel's Uniform Convergence Test
• Abel Transform
• Abhyankar's Conjecture
• Ablowitz-Ramani-Segur Conjecture
• Abscissa
• Absolute Convergence
• Absolute Deviation
• Absolute Error