scholarly journals Introducingg Complex Numbers into Basic Growth Functions (1) : Applying Complex Representation of '1' to Differentiation of Exponential Function with Base e Expanded into Infinite Series

10.5109/4593 ◽  
2004 ◽  
Vol 49 (2) ◽  
pp. 331-335
Author(s):  
Masataka Shimojo ◽  
Yoki Asano ◽  
Kentarou Ikeda ◽  
Reiko Ishiwaka ◽  
Minako Eguchi ◽  
...  
Keyword(s):  
Exponential Function ◽  
Infinite Series ◽  
Complex Representation ◽  
Complex Numbers ◽  
Growth Functions

scholarly journals On rearrangements of infinite series

1958 ◽  
Vol 3 (4) ◽  
pp. 182-193 ◽  
Author(s):  
A. P. Robertson
Keyword(s):  
Infinite Series ◽  
Convergent Series ◽  
Complex Numbers ◽  
Famous Theorem

If a convergent series of real or complex numbers is rearranged, the resulting series may or may not converge. There are therefore two problems which naturally arise.(i) What is the condition on a given series for every rearrangement to converge?(ii) What is the condition on a given method of rearrangement for it to leave unaffected the convergence of every convergent series?The answer to (i) is well known; by a famous theorem of Riemann, the series must be absolutely convergent. The solution of (ii) is perhaps not so familiar, although it has been given by various authors, including R. Rado [7], F. W. Levi [6] and R. P. Agnew [2]. It is also given as an exercise by N. Bourbaki ([4], Chap. III, § 4, exs. 7 and 8).

scholarly journals Beschreibung des Wachstums weiblicher Rinder verschiedener Rassen

1999 ◽  
Vol 42 (4) ◽  
pp. 335-346
Author(s):  
H.-D. Matthes ◽  
P. E. Rudolph
Keyword(s):  
Exponential Function ◽  
Adult Animal ◽  
Natural Growth ◽  
Growth Functions ◽  
Weight Data

Abstract. Title ofthe paper: Description on the growth of female cows of different race Continuously won weight data from the birth up to the adult animal of female cows of the races Charolais, Fleckvieh and Uckermärker were used for the determination of best fitted functions with respect to some' optimum functions from different growth-functions like exponential-, Gompertz-, logisfic-, Bertalanffy-, tanhand Janoschek-function. The four-parametric Richards- and Janoschek-function describe the natural growth (monthly increases) most exact. The exponential-function is also suitable for the describtion of the weight-development.

Simultaneous approximation of numbers connected with the exponential function

1978 ◽  
Vol 25 (4) ◽  
pp. 466-478 ◽  
Author(s):  
Michel Waldschmidt
Keyword(s):  
Lower Bounds ◽  
Exponential Function ◽  
Complex Number ◽  
Simultaneous Approximation ◽  
Complex Numbers ◽  
Linear Forms In Logarithms ◽  
Algebraic Numbers ◽  
Linear Forms

AbstractWe give several results concerning the simultaneous approximation of certain complex numbers. For instance, we give lower bounds for |a–ξo |+ | ea – ξ1 |, where a is any non-zero complex number, and ξ are two algebraic numbers. We also improve the estimate of the so-called Franklin Schneider theorem concerning | b – ξ | + | a – ξ | + | ab – ξ. We deduce these results from an estimate for linear forms in logarithms.

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