scholarly journals On the asymptotic expansion of a binomial sum involving powers of the summation index

2012 ◽  
pp. 113-123
Author(s):  
Richard B. Paris ◽  
P. J. Larcombe
Keyword(s):  
Asymptotic Expansion ◽  
Binomial Sum ◽  
Summation Index

scholarly journals ASYMPTOTICS OF A 3F2 POLYNOMIAL ASSOCIATED WITH THE CATALAN–LARCOMBE–FRENCH SEQUENCE

2006 ◽  
Vol 04 (04) ◽  
pp. 335-344
Author(s):  
NICO M. TEMME
Keyword(s):  
Asymptotic Expansion ◽  
Generating Function ◽  
Asymptotic Method ◽  
Integral Representations ◽  
Binomial Sum ◽  
Large N ◽  
Hypergeometric Polynomial ◽  
Polynomial Formula

The large n behavior of the hypergeometric polynomial [Formula: see text] is considered by using integral representations of this polynomial. This 3F2 polynomial is associated with the Catalan–Larcombe–French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function of the sequence. The results are similar to those obtained by Clark (2004) who used a binomial sum for obtaining an asymptotic expansion.

Influence of free convection on the diffusion current to a sphere in a laminar forced flow regime

1985 ◽  
Vol 50 (12) ◽  
pp. 2697-2714
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Asymptotic Expansion ◽  
Free Convection ◽  
Boundary Value Problem ◽  
Concentration Gradient ◽  
Empirical Formula ◽  
Convective Diffusion ◽  
Forced Flow ◽  
Diffusion Current ◽  
Wide Range ◽  
Free And Forced Convection

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

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