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The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
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Cited by 15 (1 self)
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The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
Stieltjes polynomials and Lagrange interpolation
 Math. Comp
, 1997
"... Abstract. Bounds are proved for the Stieltjes polynomial En+1, andlower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus poly ..."
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Cited by 11 (5 self)
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Abstract. Bounds are proved for the Stieltjes polynomial En+1, andlower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process with respect to the zeros of En+1, and for the extended Lagrange interpolation process with respect to the zeros of PnEn+1 in the uniform and weighted L p norms. The corresponding Lebesgue constants
Continuous ranking of zeros of special functions
 J. Math. Anal. Appl
"... Abstract. We reexamine and continue the work of J. Vosmansky´y [23] on the concept of continuous ranking of zeros of certain special functions from the point of view of the transformation theory of second order linear differential equations. This leads to results on higher monotonicity of such zeros ..."
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Cited by 3 (2 self)
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Abstract. We reexamine and continue the work of J. Vosmansky´y [23] on the concept of continuous ranking of zeros of certain special functions from the point of view of the transformation theory of second order linear differential equations. This leads to results on higher monotonicity of such zeros with respect to the rank and to the evaluation of some definite integrals. The applications are to Airy, Bessel and Hermite functions. 1.
Convexity properties of special functions and their zeros
 Recent progress in inequalities. Dedicated 9 Prof. Dragoslav S. Mitrinovic. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 430 1998, 309–323
, 1991
"... Abstract. Convexity properties are often useful in characterizing and nding bounds for special function and their zeros, as well as in questions concerning the existence and uniqueness of zeros in certain intervals. In this survey paper, we describe some work related to the gamma function, the qgam ..."
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Cited by 3 (0 self)
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Abstract. Convexity properties are often useful in characterizing and nding bounds for special function and their zeros, as well as in questions concerning the existence and uniqueness of zeros in certain intervals. In this survey paper, we describe some work related to the gamma function, the qgamma function, Bessel and cylinder functions and the Hermite function. 1.
Contemporary Mathematics Approximations for zeros of Hermite functions
"... Abstract. We present a convergent asymptotic formula for the zeros of the Hermite functions as λ → ∞. It is based on an integral formula due to the authors for the derivative of such a zero with respect to λ. We compare our result with those for zeros of Hermite polynomials given by P. E. Ricci. 1. ..."
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Abstract. We present a convergent asymptotic formula for the zeros of the Hermite functions as λ → ∞. It is based on an integral formula due to the authors for the derivative of such a zero with respect to λ. We compare our result with those for zeros of Hermite polynomials given by P. E. Ricci. 1.
THE INTEGRAL REPRESENTATION FOR THE PRODUCT OF TWO PARABOLIC CYLINDER FUNCTIONS Dν(x)Dν(−x) AT Re ν < 0 BY MEANS OF THE FUNDAMENTAL SOLUTION OF A LANDAUTYPE OPERATOR
, 2008
"... The fundamental solution (Green’s function) of a first order matrix ordinary differential equation arising in a Landautype problem is calculated by two methods. The coincidence of the two representations results in the integral formula for the product of two parabolic cylinder functions Dν(x)Dν(−x) ..."
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The fundamental solution (Green’s function) of a first order matrix ordinary differential equation arising in a Landautype problem is calculated by two methods. The coincidence of the two representations results in the integral formula for the product of two parabolic cylinder functions Dν(x)Dν(−x) at Reν < 0,x ∈ IR. PDMI Preprint 04/2001 mathca/0106142