A Laurent series expansion formula and its applications

1984 ◽  
Vol 93 (1) ◽  
pp. 59-62 ◽  
Author(s):  
R K Raina
Keyword(s):  
Series Expansion ◽  
Laurent Series ◽  
Expansion Formula

scholarly journals Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

2012 ◽  
Vol 2012 (6) ◽  
Author(s):  
Pierpaolo Mastrolia ◽  
Edoardo Mirabella ◽  
Tiziano Peraro
Keyword(s):  
Scattering Amplitudes ◽  
Series Expansion ◽  
Laurent Series

GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π

2012 ◽  
Vol 08 (02) ◽  
pp. 289-297 ◽  
Author(s):  
ZHI-GUO LIU
Keyword(s):  
Series Expansion ◽  
Gamma Function ◽  
Hypergeometric Series ◽  
Summation Formula ◽  
Expansion Formula ◽  
Type Series

Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan-type series for 1/π.

scholarly journals Complex blow-up in Burgers' equation: an iterative approach

1996 ◽  
Vol 54 (3) ◽  
pp. 353-362 ◽  
Author(s):  
Nalini Joshi ◽  
Johannes A. Petersen
Keyword(s):  
Holomorphic Function ◽  
Series Expansion ◽  
Laurent Series ◽  
Burgers Equation ◽  
Blow Up ◽  
Meromorphic Solution ◽  
Iterative Approach ◽  
Painlevé Test ◽  
Formal Laurent Series

We show that for a given holomorphic noncharacteristic surface S ∈ ℂ2, and a given holomorphic function on S1 there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.

SERIES EXPANSIONS OF THE GENERALIZED K-BESSEL FUNCTIONS ON SYMMETRIC CONES

2008 ◽  
Vol 06 (01) ◽  
pp. 1-10 ◽  
Author(s):  
HONGMING DING ◽  
WEI HE
Keyword(s):  
Series Expansion ◽  
Bessel Functions ◽  
Series Expansions ◽  
Symmetric Cones ◽  
Expansion Formula

In this paper, we generalize the series expansion formula of classical K-Bessel functions to symmetric cones.

Transfer Function Reduction

1976 ◽  
Vol 190 (1) ◽  
pp. 643-651 ◽  
Author(s):  
R. Whalley
Keyword(s):  
Transfer Function ◽  
Series Expansion ◽  
Laurent Series ◽  
Hankel Matrix ◽  
Rational Functions ◽  
Reduced Form ◽  
Reduced Order Models ◽  
Minimum Phase ◽  
Reduced Order

SYNOPSIS A method of generating reduced order models from the Laurent series expansion of a transfer function is examined by means of the Hankel Matrix and its correspondence to the field of rational functions. The approach enables particularly simple results to be derived regarding the composition of the reduced form and the avoidance of non minimum phase characteristics therein.

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