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A New Set of Orthogonal Polynomials for the Solution of Anharmonic Oscillator Problems

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Book cover Recent Advances in Engineering Science

Part of the book series: Lecture Notes in Engineering ((LNENG,volume 39))

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Abstract

By utilizing the symbolic algebra software REDUCE we derive a new set of non-classical orthogonal polynomials. They are orthogonal on the real line with respect to the weight function exp(−x4) and are defined explicitly by recursive identities. The effectiveness of the new orthogonal basis is demonstrated on a sample problem where eigenvalues of a sextic anharmonic oscillator are computed.

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References

  1. Hearn, A.C., Reduce User’s Manual, Rand Publication CP78 (Rev. 7/87), Santa Monica, CA, 1987.

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  2. Ari, N. and Demiralp, M., J. Math. Phys., 26, 1179–1185 (1985) and Bull. Tech. Univ. Istanbul, 36, 345-359, (1983).

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  3. Hochstadt, H., The Functions of Mathematical Physics, Dover, New York, (1986).

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Author information

Authors and Affiliations

  1. Department of Engineering Science, Lafayette College, Easton, PA, 18042, USA

    Nasit Ari

Authors
  1. Nasit Ari
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Editor information

Editors and Affiliations

  1. University of Maryland, Baltimore, MD, 21228, USA

    Severino L. Koh (Assoc. Dean of Engineering) (Assoc. Dean of Engineering)

  2. ICASE, NASA Langley Research Center, Mailstop 132 C, Hampton, VA, 23665, USA

    C. G. Speziale (Senior Staff Scientist) (Senior Staff Scientist)

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© 1989 Springer-Verlag Berlin, Heidelberg

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Ari, N. (1989). A New Set of Orthogonal Polynomials for the Solution of Anharmonic Oscillator Problems. In: Koh, S.L., Speziale, C.G. (eds) Recent Advances in Engineering Science. Lecture Notes in Engineering, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83695-4_19

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  • DOI: https://doi.org/10.1007/978-3-642-83695-4_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50721-5

  • Online ISBN: 978-3-642-83695-4

  • eBook Packages: Springer Book Archive

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