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A quadrature formula for entire functions of exponential type
Authors:
Qazi Ibadur Rahman and Gerhard Schmeisser
Journal:
Math. Comp. 63 (1994), 215-227
MSC:
Primary 65D30; Secondary 30D99, 65D32
MathSciNet review:
1234427
Full-text PDF Free Access
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Additional Information
Abstract: A quadrature formula over a semi-infinite interval for entire functions of exponential type is established. An alternative approach to a known expansion formula and an extension of it are also presented.
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exponential type, Math. Comp.
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(90g:65028), http://dx.doi.org/10.1090/S0025-5718-1990-0990602-8
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- [1]
- R. P. Boas, Jr., Entire functions, Academic Press, New York, 1954. MR 0068627 (16:914f)
- [2]
- -, Summation formulas and band-limited signals, Tôhoku Math. J. (2) 24 (1972), 121-125. MR 0330915 (48:9252)
- [3]
- R. P. Boas, Jr. and R. C. Buck, Polynomial expansions and analytic functions, Springer, Berlin, 1958. MR 0094466 (20:984)
- [4]
- C. Frappier and Q. I. Rahman, Une formule de quadrature pour les fonctions entières de type exponentiel, Ann. Sci. Math. Québec 10 (1986), 17-26. MR 841119 (88a:65031)
- [5]
- I. S. Gradstein and I. M. Ryshik, Tafeln--Tables, vol. 1 (bilingual: German-English), Harri Deutsch, Frankfurt/M., 1981. MR 671418 (83i:00012)
- [6]
- P. Henrici, Applied and computational complex analysis, vol. 1, Wiley, New York, 1974. MR 0372162 (51:8378)
- [7]
- -, Applied and computational complex analysis, vol. 2, Wiley, New York, 1977. MR 0453984 (56:12235)
- [8]
- E. Lindelöf, Le calcul des résidus, Chelsea, New York, 1947.
- [9]
- Q. I. Rahman and G. Schmeisser, Quadrature formulae and functions of exponential type, Math. Comp. 54 (1990), 245-270. MR 990602 (90g:65028)
- [10]
- G. Schmeisser and H. Schirmeier, Praktische Mathematik, de Gruyter, Berlin, 1976.
- [11]
- F. Stenger, Integration formulae based on the trapezoidal formula, J. Inst. Math. Appl. 12 (1973), 103-114. MR 0381261 (52:2158)
- [12]
- -, Numerical methods based on Whittaker cardinal, or sinc functions, SIAM Rev. 23 (1981), 165-224. MR 618638 (83g:65027)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1994-1234427-0
PII:
S 0025-5718(1994)1234427-0
Article copyright:
© Copyright 1994 American Mathematical Society
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