The generalized method of exhaustion
The method of exhaustion is generalized to a simple integration formula that is valid for the Riemann integrable functions. Both a geometric approach (following the usual procedure for the method of exhaustion) and an independent algebraic generalization approach are provided. Applications provided...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011638 |
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| _version_ | 1849405563847311360 |
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| author | Anthony A. Ruffa |
| author_facet | Anthony A. Ruffa |
| author_sort | Anthony A. Ruffa |
| collection | DOAJ |
| description | The method of exhaustion is generalized to a simple integration
formula that is valid for the Riemann integrable functions. Both
a geometric approach (following the usual procedure for the
method of exhaustion) and an independent algebraic generalization
approach are provided. Applications provided as examples include
use of the formula to generate new series for common functions as
well as computing the group velocity distribution resulting from
waves diffracted from an aperture. |
| format | Article |
| id | doaj-art-51c952c2e08c49df8e4cc028d5a8b2af |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-51c952c2e08c49df8e4cc028d5a8b2af2025-08-20T03:36:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131634535110.1155/S0161171202011638The generalized method of exhaustionAnthony A. Ruffa0Naval Undersea Warfare Center Division, 1176 Howell Street, Newport 02841-1708, RI, USAThe method of exhaustion is generalized to a simple integration formula that is valid for the Riemann integrable functions. Both a geometric approach (following the usual procedure for the method of exhaustion) and an independent algebraic generalization approach are provided. Applications provided as examples include use of the formula to generate new series for common functions as well as computing the group velocity distribution resulting from waves diffracted from an aperture.http://dx.doi.org/10.1155/S0161171202011638 |
| spellingShingle | Anthony A. Ruffa The generalized method of exhaustion International Journal of Mathematics and Mathematical Sciences |
| title | The generalized method of exhaustion |
| title_full | The generalized method of exhaustion |
| title_fullStr | The generalized method of exhaustion |
| title_full_unstemmed | The generalized method of exhaustion |
| title_short | The generalized method of exhaustion |
| title_sort | generalized method of exhaustion |
| url | http://dx.doi.org/10.1155/S0161171202011638 |
| work_keys_str_mv | AT anthonyaruffa thegeneralizedmethodofexhaustion AT anthonyaruffa generalizedmethodofexhaustion |