Now showing items 124-143 of 2221

  • Asymptotic approximations for n! 

    Paris, Richard B. (Hikari, 2011)
    Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic ...
  • Asymptotic evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities 

    Paris, Richard B. (Hikari, 2015-04-27)
    We obtain an asymptotic evaluation of the integral ʃ ∞ √2n+1 e−x2 H2 n (x) dx for n → ∞, where Hn(x) is the Hermite polynomial. This integral is used to determine the probability for the quantum harmonic oscillator in the ...
  • An asymptotic expansion for the Stieltjes constants 

    Paris, Richard B. (Hilaris, 2015)
    The Stieltjes constants γn appear in the coefficients in the Laurent expansion of the Riemann zeta function ζ(s) about the simple pole s = 1. We present an asymptotic expansion for γn as n → ∞ based on the approach described ...
  • The asymptotic expansion of a generalisation of the Euler-Jacobi series 

    Paris, Richard B. (European Journal of Pure and Applied Mathematics (EJPAM), 2016)
    We consider the asymptotic expansion of the sum Sp(a; w) = ∞Ʃ n=1 e−anp/nw as a → 0 in | arg a| <1/2π for arbitrary finite p > 0 and w > 0. Our attention is concentrated mainly on the case when p and w are both even ...
  • The asymptotic expansion of a generalised Mathieu series 

    Paris, Richard B. (Hikari, 2013)
    We obtain the asymptotic expansion of a generalised Mathieu series and its alternating variant for large complex values of the variable by means of a Mellin transform approach. Numerical examples are presented to demonstrate ...
  • Asymptotic expansion of n-dimensional Faxén-type integrals 

    Paris, Richard B. (European Journal of Pure and Applied Mathematics (EJPAM), 2010)
    The asymptotic expansion of n-dimensional extensions of Faxén’s integral In(z) are derived for large complex values of the variable z. The theory relies on the asymptotics of the generalised hypergeometric, orWright, ...
  • Asymptotics and Mellin-Barnes integrals 

    Paris, Richard B.; Kaminski, D. (Cambridge University Press, 2001)
  • The asymptotics of a generalised Beta function 

    Paris, Richard B. (Hilaris, 2015)
    We consider the generalised Beta function introduced by Chaudhry et al. [J. Comp. Appl. Math. 78 (1997) 19–32] defined by B(x, y; p) = ʃ 1 0 tx−1(1 − t)y−1 exp [−p / 4t(1 − t)] dt, where ℜ(p) > 0 and the parameters x and ...
  • The asymptotics of a new exponential sum 

    Paris, Richard B. (Elsevier, 2009-01-01)
    The absolutely convergent exponential sum [formula missing] is studied for m→+∞ and fixed p when the parameter θ is allowed to become large such that θ/m remains finite. This situation corresponds, in general, to the trace ...
  • Asymptotics of integrals of Hermite polynomials 

    Paris, Richard B. (Hikari Ltd, 2010)
    Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞,∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by ...
  • Asymptotics of the Gauss hypergeometric function with large parameters, I 

    Paris, Richard B. (Element d.o.o., 2013)
    We obtain asymptotic expansions for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+ε3λ;z) as |λ| →∞ when the εj are finite by an application of the method of steepest descents, thereby extending previous results corresponding ...
  • Asymptotics of the Gauss hypergeometric function with large parameters, II 

    Paris, Richard B. (Element d.o.o., 2013)
    We obtain asymptotic expansions by application of the method of steepest descents for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+λ;z) as |λ| → ∞ when 0<ε1 <1 and ε1 >1 where, without loss of generality, it is supposed ...
  • The asymptotics of the generalised Hermite–Bell polynomials 

    Paris, Richard B. (Elsevier, 2009-10-15)
    The Hermite–Bell polynomials are defined by [formula missing] for n=0,1,2,… and integer r≥2 and generalise the classical Hermite polynomials corresponding to r=2. We obtain an asymptotic expansion for [formula missing] as ...
  • The asymptotics of the mittag-leffler polynomials 

    Paris, Richard B. (Element d.o.o., 2012)
    We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π . A summary of the asymptotic properties of Gn(ix) for real ...
  • The asymptotics of the mittag-leffler polynomials 

    Paris, Richard B. (Journal of classical analysis, 2012)
    We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π . A summary of the asymptotic properties of Gn(ix) for real ...
  • ATM in focus: a damage sensor and cancer target 

    Khalil, Hilal S.; Tummala, Hemanth; Zhelev, Nikolai Z. (Dundee Science Press, 2012-11-30)
    The ability of a cell to conserve and maintain its native DNA sequence is fundamental for the survival and normal functioning of the whole organism and protection from cancer development. Here we review recently obtained ...
  • Atmospheric aerosol source identification and estimates of source contributions to air pollution in Dundee, UK 

    Qin, Y.; Oduyemi, Kehinde O. K. (Elsevier, 2003-04)
    Anthropogenic aerosol (PM10) emission sources sampled at an air quality monitoring station in Dundee have been analysed. However, the information on local natural aerosol emission sources was unavailable. A method that ...
  • Atomic force microscopic investigation of commercial pressure sensitive adhesives for forensic analysis 

    Canetta, Elisabetta; Adya, Ashok K. (Elsevier, 2011-07)
    Pressure sensitive adhesive (PSA), such as those used in packaging and adhesive tapes, are very often encountered in forensic investigations. In criminal activities, packaging tapes may be used for sealing packets containing ...
  • Atomic force microscopic study of the effects of ethanol on yeast cell surface morphology 

    Canetta, Elisabetta; Adya, Ashok K.; Walker, Graeme M. (Blackwell Publishing, 2006-02)
    The detrimental effects of ethanol toxicity on the cell surface morphology of Saccharomyces cerevisiae (strain NCYC 1681) and Schizosaccharomyces pombe (strain DVPB 1354) were investigated using an atomic force microscope ...
  • Atomic force microscopic study of the influence of physical stresses on Saccharomyces cerevisiae and Schizosaccharomyces pombe 

    Adya, Ashok K.; Canetta, Elisabetta; Walker, Graeme M. (Blackwell Publishing, 2006-01)
    Morphological changes in the cell surfaces of the budding yeast Saccharomyces cerevisiae (strain NCYC 1681), and the fission yeast Schizosaccharomyces pombe (strain DVPB 1354), in response to thermal and osmotic stresses, ...