Estimates of sums of integrals of Legendre polynomial

Authors

  • Konstantin V. Kholshevnikov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Tomsk State University, pr. Lenina, 36, Tomsk, 634050, Russian Federation; Main (Pulkovo) Observatory RAS, Pulkovskoe chaussee, 65/1, St. Petersburg, 196140, Russian Federation;
  • Vakhit Sh. Shaidulin St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Tomsk State University, pr. Lenina, 36, Tomsk, 634050, Russian Federation; Main (Pulkovo) Observatory RAS, Pulkovskoe chaussee, 65/1, St. Petersburg, 196140, Russian Federation;

DOI:

https://doi.org/10.21638/11701/spbu01.2016.208

Abstract

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References

Литература

1. Гобсон Е.В. Теория сферических и эллипсоидальных функций. М.: ИЛ, 1952, 476 с.

2. Сегё Г. Ортогональные многочлены. М.: ФМ, 1962. 500 с.

3. Холшевников К.В., Шайдулин В.Ш. Асимптотика интегралов от многочлена Лежандра и их сумм // Вестник С-Петерб. ун-та. Сер. 1. 2015. Т. 2(60), вып. 4. C. 553-562.

4. Холшевников К.В., Шайдулин В.Ш. О свойствах интегралов от многочлена Лежандра // Вестник С-Петерб. ун-та. Сер. 1. 2014. Т. 1(59), вып. 1. C. 55-67.

5. Бейтмен Г., Эрдейи А. Высшие трансцендентные функции. Гипергеометрическая функция. Функции Лежандра. М.: Наука, 1965. 296 с.

6. Градштейн И.С., Рыжик И.М. Таблицы интегралов, сумм, рядов и произведений. М.: Наука, 1971. 1108 с.

References

1. Hobson E. W., The Theory of Spherical and Ellipsoidal Harmonics (Cambridge, Cambridge Univ. Press, 1931. 476 p.).

2. Szeg¨o G., Orthogonal polynomials 23 (AMS Colloquium publ., 1975, 432 p.).

3. Kholshevnikov K.V., Shaidulin V. Sh., “Asymptotic behaviour of integrals of Legendre polynomial and their sums”, Vestnik St.Petersburg University: Mathematics 48, Issue 4, 233–240 (2015).

4. Kholshevnikov K.V., Shaidulin V. Sh., “On Properties of Integrals of the Legendre Polynomial”, Vestnik St.Petersburg University: Mathematics 47, Issue 1, 28–38 (2014).

5. Bateman H., Erd´elyi A., Higher Transcendental Functions 1 (McGraw-Hill, New York, Toronto, London, 1953, 298 p.).

6. Gradsteyn I. S., Ryzhik I.M., Table of Integrals, Series, and Products (Eds. D. Zwillinger and V.Moll, 2014, 1184 p.). 252

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Published

2020-10-19

How to Cite

Kholshevnikov, K. V., & Shaidulin, V. S. (2020). Estimates of sums of integrals of Legendre polynomial. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 3(2), 1. https://doi.org/10.21638/11701/spbu01.2016.208

Issue

Vol. 3 No. 2 (2016)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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