Definite integrals using orthogonality and integral transforms
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012)

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We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
Keywords: definite integrals; associated Legendre functions; Bessel functions; Chebyshev polynomials of the first kind.
Howard S. Cohl; Hans Volkmer. Definite integrals using orthogonality and integral transforms. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a76/
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[1] Abramowitz M., Stegun I.A., Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, 55, U.S. Government Printing Office, Washington, DC, 1964 | MR

[2] Askey R., Orthogonal polynomials and special functions, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975 | MR | Zbl

[3] Cohl H.S., Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems, arXiv: 1209.6047

[4] Cohl H.S., “Erratum: Developments in determining the gravitational potential using toroidal functions”, Astronom. Nachr., 333 (2012), 784–785 | DOI

[5] Cohl H.S., Dominici D.E., “Generalized Heine's identity for complex Fourier series of binomials”, Proc. R. Soc. Lond. Ser. A, 467 (2011), 333–345 ; arXiv: 0912.0126 | DOI | MR | Zbl

[6] Cohl H.S., Tohline J.E., Rau A.R.P., Srivastava H.M., “Developments in determining the gravitational potential using toroidal functions”, Astronom. Nachr., 321 (2000), 363–372 | 3.0.CO;2-X class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | Zbl

[7] Gradshteyn I.S., Ryzhik I.M., Table of integrals, series, and products, seventh ed., Elsevier/Academic Press, Amsterdam, 2007 | MR | Zbl

[8] Hardy G.H., “Further researches in the theory of divergent series and integrals”, Trans. Cambridge Philos. Soc., 21 (1908), 1–48

[9] MacRobert T.M., Spherical harmonics. An elementary treatise on harmonic functions with applications, 2nd ed., Methuen Co. Ltd., London, 1947 | MR

[10] Magnus W., Oberhettinger F., Soni R.P., Formulas and theorems for the special functions of mathematical physics, Die Grundlehren der mathematischen Wissenschaften, 52, 3rd ed., Springer-Verlag, New York, 1966 | MR | Zbl

[11] Morse P.M., Feshbach H., Methods of theoretical physics, v. 1, 2, McGraw-Hill Book Co. Inc., New York, 1953 | MR | Zbl

[12] Olver F.W.J., Lozier D.W., Boisvert R.F., Clark C.W. (Eds.), NIST handbook of mathematical functions, Cambridge University Press, Cambridge, 2010 | MR | Zbl

[13] Prudnikov A.P., Brychkov Y.A., Marichev O.I., Integrals and series, v. 3, More special functions, Gordon and Breach Science Publishers, New York, 1990 | MR | Zbl

[14] Schäfke F.W., Einführung in die Theorie der speziellen Funktionen der mathematischen Physik, Die Grundlehren der mathematischen Wissenschaften, 118, Springer-Verlag, Berlin, 1963 | MR

[15] Watson G.N., A treatise on the theory of Bessel functions, Cambridge Mathematical Library, 2nd ed., Cambridge University Press, Cambridge, 1944 | MR | Zbl