Advanced search
Publication Cover
Transactions of the Royal Society of South Africa Volume 77, 2022 - Issue 1
Submit an article Journal homepage
64
Views
0
CrossRef citations to date
0
Altmetric
Regular Articles

On elementary complex variable theory applied to generalised sinc(p) and related integrals

J. D. Hey Mem. R. S. S. Af.School of Chemistry and Physics, University of KwaZulu-Natal, Durban, South AfricaCorrespondence[email protected] [email protected]
ORCID Iconhttps://orcid.org/0000-0003-3651-3660
ORCID Icon
Pages 11-25 | Published online: 10 Jan 2022

References

  • Abramowitz, M. & Stegun, I.A. (Ed.). 1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Ch. 6. New York, Dover.
  • Baez, J.C. 2018. Patterns that Eventually Fail. Azimuth Project. https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/
  • Borwein, D. & Borwein, J.M. 2001. Some remarkable properties of sinc and related integrals. The Ramanujan Journal 5: 73–89.
  • Bromwich, T.J.I’A. 1926. An Introduction to the Theory of Infinite Series (2nd ed., revised by T. M. MacRobert & H. T. Croft). London, Macmillan.
  • Byron Jr, F.W. & Fuller, R.W. 1970. Mathematics of Classical and Quantum Physics, Vol. II, Ch. 6. Reading, Massachusetts, Addison-Wesley.
  • Chandrasekhar, S. 1943. Stochastic problems in physics and astronomy. Reviews of Modern Physics 15(1): 1–89.
  • Copson, E.T. 1962. An Introduction to the Theory of Functions of a Complex Variable. Oxford, Clarendon Press.
  • Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F.G. 1954. Tables of Integral Transforms, Vol. I. New York, McGraw-Hill. pp. 68, 78, 79.
  • Griem, H.R. 1974. Spectral Line Broadening by Plasmas (Ch. II). New York, Academic Press.
  • Hahn, B. 1994. C++: A Practical Introduction. Oxford, Blackwell.
  • Hey, J.D. 1976. Ion dynamical corrections to the Holtsmark theory of spectral line broadening. Transactions of the Royal Society of South Africa 42(1): 81–101.
  • Hey, J.D. 2012. On the role of atomic metastability in the production of Balmer line radiation from ‘cold’ atomic hydrogen, deuterium and hydrogenic ion impurities in fusion edge plasmas. Journal of Physics B: Atomic, Molecular and Optical Physics 45: 065701 (19 pp.).
  • Hey, J.D. 2015 On the Runge-Lenz-Pauli vector operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas. Journal of Physics B: Atomic, Molecular and Optical Physics 48: 185701 (16 pp.)
  • Hey, J.D. 2020. On elementary complex variable theory applied to sinc and related integrals. Transactions of the Royal Society of South Africa 75(3): 295–306.
  • Hill, H.M. 2019. Random walkers illuminate a math problem: a family of tricky integrals can now be solved without explicit calculation. Physics Today 72(9): 18–19.
  • Hochstadt, H. 1986. The Functions of Mathematical Physics. New York, Dover.
  • Holtsmark, J. 1919a. Ṻber die Verbreiterung von Spektrallinien. Physikalische Zeitschrift 20: 162–168.
  • Holtsmark, J. 1919b. Ṻber die Verbreiterung von Spektrallinien. Annalen der Physik (Ser. IV) 58: 577–630.
  • Holtsmark, J. 1924. Ṻber die Verbreiterung von Spektrallinien. II. Physikalische Zeitschrift 25: 73–84.
  • Irving, J. & Mullineux, N. 1959. Mathematics in Physics and Engineering. New York, Academic Press.
  • Landau, L.D., Lifshitz, E.M. & Pitaevskii, L.P. 1977. Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (translated by J. B. Sykes and J. S. Bell). Oxford, Pergamon.
  • Lebedev, N.N. 1972. Special Functions and their Applications (translated by R. A. Silverman). New York, Dover.
  • Loney, S.L. 1900. Plane Trigonometry. Cambridge, Cambridge University Press.
  • Lord, N. 2007. An amusing sequence of trigonometrical integrals. The Mathematical Gazette 91: 281–285.
  • Majumdar, S.N. & Trizac, E. 2019. When random walkers help solving intriguing integrals. Physical Review Letters 123: 020201 (5 pp.)
  • Pascal, Blaise. 1665. Traite du Triangle Arithmétique, avec Quelques Autres Petits Traitez sur la Mesme Matière. Par Monsieur Pascal. Paris, Guillaume Desprez.
  • Peirce, B.O. & Foster, R.M. 1956. A Short Table of Integrals, 4th ed. Boston, Ginn. pp. 69, 70.
  • Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T. 1986. Numerical Recipes: the Art of Scientific Computing. Cambridge, Cambridge University Press.
  • Schmid, H. 2014. Two curious integrals and a graphic proof. Elemente der Mathematik 69: 11–17
  • Spiegel, M.R. 1964. Complex Variables with an Introduction to Conformal Mapping and its Applications. New York, Schaum.
  • Stőrmer, C. 1895. Sur une généralisation de la formule φ2=sin⁡φ1−sin⁡2φ2+sin⁡3φ3−⋅⋅⋅. Acta Mathematica 19: 341–350.
  • Weast, R.C. (ed.). 1974. Handbook of Chemistry and Physics. Cleveland, Ohio, CRC Press. p. A-163.
  • Whittaker, E.T. & Watson, G.N. 1927. A Course of Modern Analysis, Ch. VI (4th ed.). Cambridge, Cambridge University Press.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.