Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model Problems

Mathematics – Numerical Analysis

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

25 pages, 7 tables, REVTeX

Scientific paper

10.1016/S0010-4655(00)00175-2

Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain asymptotic regularities normally do exist, but the leading elements of a sequence may behave quite irregularly. The Gaussian hypergeometric series 2F1 (a, b; c; z) is well suited to illuminate problems of that kind. Sequence transformations perform quite well for most parameters and arguments. If, however, the third parameter $c$ of a nonterminating hypergeometric series 2F1 is a negative real number, the terms initially grow in magnitude like the terms of a mildly divergent series. The use of the leading terms of such a series as input data leads to unreliable and even completely nonsensical results. In contrast, sequence transformations produce good results if the leading irregular terms are excluded from the transformation process. Similar problems occur also in perturbation expansions. For example, summation results for the infinite coupling limit k_3 of the sextic anharmonic oscillator can be improved considerably by excluding the leading terms from the transformation process. Finally, numerous new recurrence formulas for the 2F1 (a, b; c; z) are derived.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model Problems will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-291479

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.