A probabilistic interpretation of a modified Gegenbauer polynomial is furnished by its expression in terms of a combinatorial probability defined on a compound urn model. Also, a combinatorial interpretation of its coefficients is provided. In particular, probabilistic interpretations of a modified Chebyshev polynomial of the second kind and a modified Legendre polynomial together with combinat...

An operational approach introduced by Gould and Hopper to the construction of generalized Hermite polynomials is followed in the hypercomplex context to build multidimensional generalized Hermite polynomials by the consideration of an appropriate basic set of monogenic polynomials. Directly related functions, like Chebyshev polynomials of first and second kind are constructed.

The effect of the Transcendental Meditation (TM) technique on working memory and field independence was investigated in a twelve-week longitudinal time-series study in which the uMatch Me" computerized memory game and the Rod and Frame Test were administered daily to a matched pair of 11-year-old boys and a matched pair of 14-year-old girls. One of the boys and one of the girls began the TM tec...

with given a, b, t0, t1 and n ≥ 0. This sequence was introduced by Horadam [3] in 1965, and it generalizes many sequences (see [1, 4]). Examples of such sequences are Fibonacci polynomials sequence (Fn(x))n≥0, Lucas polynomials sequence (Ln(x))n≥0, and Pell polynomials sequence (Pn(x))n≥0, when one has a = x, b = t1 = 1, t0 = 0; a = t1 = x, b = 1, t0 = 2; and a = 2x, b = t1 = 1, t0 = 0; respect...

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain q-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the q-Laguerre and the q-Charlier polynomials, in the style of the Touchard...

We consider a fourth-order eigenvalue problem on a semi-infinite strip which arises in the study of viscoelastic shear flow. The eigenvalues and eigenfunctions are computed by a spectral method involving Laguerre functions and Legendre polynomials.

We develop polynomials in z ∈ C for which some generalized harmonic numbers are special cases at z= 0. By using the Riordan array method, we explore interesting relationships between these polynomials, the generalized Stirling polynomials, the Bernoulli polynomials, the Cauchy polynomials and the Nörlund polynomials. © 2007 Elsevier B.V. All rights reserved.

; Factorial () ; Factorial calculates the factorial of an input ; integer given in the AX register and returns the ; result in the AX register. Assumes input is ; nonnegative. Factorial PUSHA ; Save all registers on stack MOV CX,AX ; Initialize loop counter MOV AX,0 ; Initialize result CMP CX,0 ; Check for zero case JE .Done .Factorialloop: MUL CX ; AX = AX * CX LOOP Factorial ; Decrement CX, j...

BACKGROUND The 2 × 2 factorial design is widely used for assessing the existence of interaction and the extent of generalizability of two factors where each factor had only two levels. Accordingly, research problems associated with the main effects and interaction effects can be analyzed with the selected linear contrasts. METHODS To correct for the potential heterogeneity of variance structu...

A novel, supersaturable self-microemulsifying drug delivery system (S-SMEDDS) was successfully formulated to enhance the dissolution and oral absorption of valsartan (VST), a poorly water-soluble drug, while reducing the total quantity for administration. Poloxamer 407 is a selectable, supersaturating agent for VST-containing SMEDDS composed of 10% Capmul® MCM, 45% Tween® 20, and 45% Transcutol...