Geodesic
Some integral equations involving finite parts of divergent integrals
Glasgow mathematical journal, Tome 8 (1967) no. 1, pp. 50-54

Voir la notice de l'article provenant de la source Cambridge University Press

In recent years, a number of special integral equations of the first kind was discussed by several authors (see [l]–[4], [6], [7], [9]–[18]). The kernels of these integral equations are special functions of the hypergeometric family, and it was necessary to restrict the parameters appearing in these functions to secure convergence of the integrals. If these restrictions are removed, the integral fails to converge but it may possess a finite part (in Hadamard's sense), and the question arises whether the methods used in the restricted case will alsoapply in the new situation. Indeed, one could pose the moregeneral problem of Volterra integral equations involving finite parts of divergent integrals [19] 
Erdélyi, A. Some integral equations involving finite parts of divergent integrals. Glasgow mathematical journal, Tome 8 (1967) no. 1, pp. 50-54. doi: 10.1017/S0017089500000070
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[1] 1.Buschman, R. G., An inversion integral for a Legendre transformation, Amer. Math. Monthly 69 (1962), 288–289. Google Scholar | DOI

[2] 2.Buschman, R. G., An inversion integral, Proc. Amer. Math. Soc. 13 (1962), 675–677. Google Scholar | DOI

[3] 3.Buschman, R. G., An inversion integral for a general Legendretransformation, SIAM Rev. 5 (1963), 232–233. Google Scholar | DOI

[4] 4.Buschman, R. G., Convolution equations with generalized Laguerre polynomial kernels, SIAM Rev. 6 (1964), 166–167. Google Scholar | DOI

[5] 5.Butzer, P. L., Singular integral equations of Volterra type and the finite part of divergent integrals, Arch. Rational Mech. Anal. 3 (1959), 194–205. Google Scholar | DOI

[6] 6.Erdelyi, A., An integral equation involving Legendre's polynomial, Amer. Math. Monthly 70 (1963), 651–652. Google Scholar | DOI

[7] 7.Erdélyi, A., An integral equation involving Legendre functions, J. Soc. Indust. Appl. Math. 12 (1964), 15–30. Google Scholar | DOI

[8] 8.Gelfand, I. M. and Shilov, G. E., Generalized functions, vol. I (Academic Press, New York and London, 1964). Google Scholar

[9] 9.Higgins, T. P., An inversion integral for a Gegenbauer transformation, J. Soc. Indust. Appl. Math. 11 (1963), 886–893. Google Scholar | DOI

[10] 10.Higgins, T. P., A hypergeometric function transform, J. Soc. Indust. Appl. Math. 12 (1964), 601–612. Google Scholar | DOI

[11] 11.Li, Ta, A new class of integral transforms. Proc. Amer. Math. Soc. 11 (1960), 290–298. Google Scholar | DOI

[12] 12.Love, E. R., Some integral equations involving hypergeometric functions; to appear in Proc. Edinburgh Math. Soc. Google Scholar

[13] 13.Srivastava, K. N., On some integral transforms, Math. Japon. 6 (1961–1962), 65–72. Google Scholar

[14] 14.Srivastava, K. N., A class of integral equations involving ultraspherical polynomials as kernel, Proc. Amer. Math. Soc. 14 (1963), 932–940. Google Scholar | DOI

[15] 15.Srivastava, K. N., Inversion integrals involving Jacobi's polynomials, Proc. Amer. Math. Soc. 15 (1964), 635–638. Google Scholar

[16] 16.Srivastava, K. N., On some integral transforms involving Jacobi functions, Ann. Polon. Math. 16 (1965), 195–199. Google Scholar | DOI

[17] 17.Srivastava, K. N., On integral equations involving Whittaker's function, Proc. Glasgow Math. Assoc. 7 (1966), 125–127. Google Scholar | DOI

[18] 18Wimp, Jet, Two integral transform pairs involving hypergeometric functions, Proc. Glasgow Math. Assoc. 7 (1965), 42–4. Google Scholar | DOI

[19] 19.Wiener, Klaus, Lineare Integralgleichungen mit Hadamard-Integralen, Wiss. Z. Martin- Luther-Univ. Halle-Wittenberg. Math.-Nat. Reihe 11 (1962), 567–580. Google Scholar

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