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Moment integrals of powers of airy functions

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Abstract

Difference equations for moment integrals which contain powers of the Airy functionAi(z) and its derivativeAi'(z) i.e.

$$\int_0^\infty {z^n [Ai(z)]^\alpha dz,} \int_0^\infty {z^n [Ai'(z)]^\alpha dz,} $$

are obtained. These equations are easily solved for the special case of integer α. The moments occur in recent analytical attempts at solving certain nonlinear problems in Physics and Chemistry.

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References

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  1. Dept of Chemistry, State University of New York at Albany, 12222, Albany, New York, USA

    Bernard J. Laurenzi

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  1. Bernard J. Laurenzi
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Laurenzi, B.J. Moment integrals of powers of airy functions. Z. angew. Math. Phys. 44, 891–908 (1993). https://doi.org/10.1007/BF00942815

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  • DOI: https://doi.org/10.1007/BF00942815

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