scholarly journals ANALYTICAL EVALUATION OF THE EINSTEIN INTEGRATE USING BINOMIAL EXPANSION THEOREM AND POWER SERIES

2018 ◽  
Vol 6 (2) ◽  
pp. 1-1
Author(s):  
Hüseyin KOÇ
Keyword(s):  
Power Series ◽  
Analytical Evaluation ◽  
Expansion Theorem ◽  
Binomial Expansion

Use of complete gamma function in accurate evaluation of Einstein integrals

2008 ◽  
Vol 39 (3) ◽  
pp. 223-227
Author(s):  
I. I. Guseinov ◽  
B. A. Mamedov
Keyword(s):  
Sediment Transport ◽  
Series Expansion ◽  
Gamma Function ◽  
Numerical Calculations ◽  
Computational Time ◽  
Expansion Theorem ◽  
Accurate Evaluation ◽  
Modern Sediment ◽  
Binomial Expansion

By the use of the binomial expansion theorem, the series expansion relations in terms of the complete gamma function are obtained for Einstein integrals arising in the hydraulic and modern sediment transport mechanics. The approach presented for Einstein integrals is accurate enough over the whole range of parameters. The computational time for calculation of the series with respect to the literature is fast. Furthermore, the comparison of the method with numerical calculations demonstrates the applicability and accuracy of the method.

scholarly journals A general formula for calculation of the two-dimensional Franck–Condon factors

2017 ◽  
Vol 95 (4) ◽  
pp. 340-345 ◽  
Author(s):  
H. Koç ◽  
B.A. Mamedov ◽  
E. Eser
Keyword(s):  
Hermite Polynomials ◽  
Analytical Formula ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Expansion Theorem ◽  
Binomial Expansion ◽  
Condon Factors ◽  
Astrophysical Molecules ◽  
Franck Condon ◽  
Kinetics Of

Knowledge of the Franck–Condon factors (FCFs) and related quantities is essential to understand and to estimate many important aspects of the astrophysical molecules, such as kinetics of the energy transfer, radiative lifetimes, band intensity, and vibrational temperatures. In this view, we propose a new analytical formula of the Franck–Condon integral for two-dimensional harmonic oscillators taking into account the Duschinsky effect. This method is based on the use of the binomial expansion theorem and the Hermite polynomials. With the formula obtained, the FCF of any transition can be computed independently. In this study, the method for FCF calculations was applied to the NO2molecule.

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