On a Class of Iteration Formulas and Some Historical Notes

The class of iteration formulas obtainable
by rational approximations of "Euler's formula" 
is derived with the corresponding error estimates. 
Some historical notes on iterative procedures are 
followed by a derivation of Euler's formula with the
associated error estimate in a new notation which 
simplifies the error estimate and suggests generalizations.
 The final section considers the Pade approximants 
to the "Euler polynomial" and shows how a number of known
formulas may be derived from this unified approach. 
 There is a short discussion of the "best" formula.

CACM June, 1961

Traub, J. F.

CA610606 JB March 16, 1978  10:36 PM

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