Accession Number : AD0430761


Title :   A CONDITION NECESSARY AND SUFFICIENT FOR A FUNCTION TO BE EQUAL TO ITS CONTINUED FRACTION EXPANSION. APPENDIX: THE EFFECT OF REMAINDERS ON CONVERGENCE,


Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER


Personal Author(s) : LANE,Ralph E ; Hayden,T L


Report Date : Nov 1963


Pagination or Media Count : 28


Abstract : The problem of whether or not a continued fraction expansion for a specified function is equal to that function is solved in terms of the remainders of the expansion. A method of expanding a continued fraction is given, which has application to many other functions, and the results of the previous sections are applied to show that the expansion is equal to the given function. A method of obtaining approximations of specified accuracy is also given. In the appendix various expansions are obtained for the remainders of the example considered and the effect of these remainders on the rate of convergence is considered. (Author)


Descriptors :   *FUNCTIONS(MATHEMATICS) , NUMBERS , ERRORS , SERIES(MATHEMATICS)


Distribution Statement : APPROVED FOR PUBLIC RELEASE