Application of a certain integral formula to complex analysis

1991 ◽  
pp. 94-114 ◽  
Author(s):  
Kensho Takegoshi
Keyword(s):  
Complex Analysis ◽  
Integral Formula

scholarly journals Deriving Cauchy's Integral Formula Using Division Method

2019 ◽  
Vol 1 ◽  
pp. 259-264
Author(s):  
M Egahi ◽  
I O Ogwuche ◽  
J Ode
Keyword(s):  
Analytic Functions ◽  
Complex Analysis ◽  
Integral Formula ◽  
Integral Theorem ◽  
Cauchy’S Integral Formula ◽  
Cauchy’S Integral Theorem

Cauchy's integral theorem and formula which holds for analytic functions is proved in most standard complex analysis texts. The nth derivative form is also proved. Here we derive the nth derivative form of Cauchy's integral formula using division method and showed its link with Taylor's theorem and demonstrate the result with some polynomials.

Properties of isolated singularities of some functions taking values in real Clifford algebras

1984 ◽  
Vol 95 (2) ◽  
pp. 277-298 ◽  
Author(s):  
John Ryan
Keyword(s):  
Differential Equations ◽  
Clifford Algebras ◽  
Complex Analysis ◽  
Integral Formula ◽  
Theoretical Physics ◽  
Natural Manner ◽  
Expansion Theorem ◽  
Yang Mills ◽  
Elliptic Differential Equations ◽  
Mills Field

The study of solutions to special examples of elliptic differential equations, using Clifford algebras, has been developed by a number of authors [4–12, 14–16, 18, 19, 21–30, 32]. This study has also been applied [3, 13, 17, 28] within a number of areas of theoretical physics, including Yang–Mills field theory, and the Kähler equation. Most of the function theories associated to the solutions of these elliptic differential equations, referred to as generalized Cauchy–Riemann equations [21,32], generalize in a natural manner many aspects of classical one-variable complex analysis [1]. For instance, each of these function theories contain analogues of the Cauchy theorem, Cauchy integral formula and Laurent expansion theorem. However, no information has yet been obtained on the local topological behaviour of a general solution to any of these equations.

scholarly journals A further generalization of the Catalan numbers and its explicit formula and integral representation

2021 ◽  
Author(s):  
Wen-Hui Li ◽  
Feng Qi ◽  
Omran Kouba ◽  
Issam Kaddoura
Keyword(s):  
Number Theory ◽  
Integral Representation ◽  
Explicit Formula ◽  
Generating Function ◽  
Complex Analysis ◽  
Integral Formula ◽  
Catalan Numbers ◽  
Combinatorial Number Theory ◽  
Integral Formulas ◽  
Cauchy’S Integral Formula

In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy’s integral formula in complex analysis, the authors generalize the Catalan numbers and its generating function, establish an explicit formula and an integral representation for the generalization of the Catalan numbers and corresponding generating function, and derive several integral formulas and combinatorial identities.

scholarly journals A further generalization of the Catalan numbers and its explicit formula and integral representation

2020 ◽  
Author(s):  
Wen-Hui Li ◽  
Feng Qi ◽  
Omran Kouba ◽  
Issam Kaddoura
Keyword(s):  
Number Theory ◽  
Integral Representation ◽  
Explicit Formula ◽  
Generating Function ◽  
Complex Analysis ◽  
Integral Formula ◽  
Catalan Numbers ◽  
Combinatorial Number Theory ◽  
Integral Formulas ◽  
Cauchy’S Integral Formula

In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy's integral formula in complex analysis, the authors generalize the Catalan numbers and its generating function, establish an explicit formula and an integral representation for the generalization of the Catalan numbers and corresponding generating function, and derive several integral formulas and combinatorial identities.

An integral formula for the even part of the texture function or « the apparition of the fπ and fω ghost distributions »

1982 ◽  
Vol 43 (2) ◽  
pp. 189-195 ◽  
Author(s):  
Claude Esling ◽  
Jacques Muller ◽  
Hans-Joachim Bunge
Keyword(s):  
Integral Formula

Effect of Calcium ion on the interaction between Thrombin and Heparin. Thermal Denaturation

1977 ◽  
Vol 38 (03) ◽  
pp. 0677-0684 ◽  
Author(s):  
Raymund Machovich ◽  
Péter Arányi
Keyword(s):  
Calcium Ions ◽  
Rate Constants ◽  
Thermal Denaturation ◽  
Time Course ◽  
Complex Analysis ◽  
Heat Inactivation ◽  
Second Phase ◽  
Denaturation Kinetics ◽  
Enzyme Protection ◽  
Enzyme Denaturation

SummaryHeat inactivation of thrombin at 54° C followed first order kinetics with a rate constant of 1.0 min−1 approximately. Addition of heparin resulted in protection against thermal denaturation and, at the same time, rendered denaturation kinetics more complex. Analysis of the biphasic curve of heat inactivation in the presence of heparin revealed that the rate constants of the second phase changed systematically with heparin concentrations. Namely, at 4.5 × 10−6M, 9 × 10−6M, 1.8 × 10−5M and 3.6 × 10−5M heparin concentrations, the rate constants were 0.27 min−1, 0.17 min−1, 0.11 min−1 and 0.06 min−1, respectively.Sulfate as well as phosphate ions displayed also enzyme protection against heat inactivation, however, the same effect was obtained already at a heparin concentration, lower by three orders of magnitude.The kinetics of enzyme denaturation was not affected by calcium ions, whereas in the presence of heparin the inactivation rate of thrombin changed, i. e. calcium ions abolished the biphasic character of time course of thermal denaturation.Thus, the data suggest that calcium ions contribute to the effect of heparin on thrombin.

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