Laguerre polynomials - Open Access .click

SIAM Journal on Mathematical Analysis, 1993
The authors investigate orthogonal polynomials for the inner product \[ \langle p,q\rangle= \int_ 0^ \infty {x^ \alpha e^{-x}\over \Gamma(\alpha+1)} p(x)q(x) dx+Mp(0)q(0) + Np'(0) q'(0), \] thereby generalizing the Laguerre polynomials $(M=N=0)$ and Koornwinder's Laguerre-type polynomials $(N=0)$.
Koekoek, R., Meijer, H. G.
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On an integral of product of laguerre polynomials

International Journal of Computer Mathematics, 1997
The evaluation of an integral of the product of Laguerre polynomials which appeared recently in this Journal by Mavromatis [36, 1990, p. 257] is shown to be a particular case of a general result of Erdelyi. An error in the special case derived earlier and other possible explicit evaluations on account of special forms of the 3 F 2(1) function are ...
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On series representation in laguerre polynomials

Complex Variables, Theory and Application: An International Journal, 1993
This paper concerns with the existence of singularities of the series \[ \sum^ \infty_{n=0} a_ n L^{(\alpha)}_ n(z)\quad (\alpha\neq - 1,-2,\ldots) \] on the boundary of the region of convergence under certain assumptions on the coefficients.
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Integrals of Products of Laguerre Polynomials

SIAM Journal on Mathematical Analysis, 1975
If $L_n(x)$ is the nth Laguerre polynomial, let $A_{rst} (\alpha ) = \int _0^\infty e^{ - \alpha x} L_r (x)L_s (x)L_t (x)dx$. It has recently been shown that $A_{rst} (\alpha ) > 0$ for $\alpha \geqq 2,r,s,t = 0,1, \cdots $, while $( - 1)^{r + s + t} A_{rst} (\alpha ) \geqq 0$ for $0 0$ for $r \geqq t$. The complete conjecture has not yet been proved,
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