Accession Number : AD0657567

Title :   SUMMATION OF SERIES OF POSITIVE TERMS BY CONDENSATION TRANSFORMATIONS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Daniel,James W.

Report Date : APR 1967

Pagination or Media Count : 17

Abstract : The condensation transformation, which maps series of positive terms into more conveniently summed alternating series, each term v sub j of which is itself an infinite series, is discussed with examples. It is shown that for a large class of extremely slowly convergent series (essentially those dominated by the 'logarithmic scale') the series defining the terms v sub j are more easily summed than the original and may in fact be transformed further if desired. Numerical examples reveal the power of the method. (Author)

Descriptors :   (*SERIES(MATHEMATICS), CONVERGENCE), (*TRANSFORMATIONS(MATHEMATICS), SERIES(MATHEMATICS)), NUMERICAL ANALYSIS, SEQUENCES(MATHEMATICS), ALGORITHMS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE