scholarly journals Integral representations of functions and Addison-type series for mathematical constants

2015 ◽  
Vol 157 ◽  
pp. 79-98 ◽  
Author(s):  
Mark W. Coffey
Keyword(s):  
Integral Representations ◽  
Type Series ◽  
Mathematical Constants

Series representing transcendental numbers that are not U-numbers

2015 ◽  
Vol 11 (03) ◽  
pp. 869-892
Author(s):  
Emre Alkan
Keyword(s):  
Rational Functions ◽  
Rational Numbers ◽  
Upper Bounds ◽  
Integral Representations ◽  
Binomial Coefficients ◽  
Elementary Functions ◽  
Linear Combinations ◽  
Type Series ◽  
Transcendental Numbers ◽  
Mathematical Constants

Using integral representations with carefully chosen rational functions as integrands, we find new families of transcendental numbers that are not U-numbers, according to Mahler's classification, represented by a series whose terms involve rising factorials and reciprocals of binomial coefficients analogous to Apéry type series. Explicit descriptions of these numbers are given as linear combinations with coefficients lying in a suitable real algebraic extension of rational numbers using elementary functions evaluated at arguments belonging to the same field. In this way, concrete examples of transcendental numbers which can be expressed as combinations of classical mathematical constants such as π and Baker periods are given together with upper bounds on their wn measures.

scholarly journals New integral and series representations of the generalized Mathieu series

2008 ◽  
Vol 2 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Zivorad Tomovski
Keyword(s):  
Integral Representations ◽  
Type Series ◽  
Fourier Sine ◽  
Series Representations ◽  
Mathieu Series

By using some recently investigated fourier sine integral representations for the Mathieu type series (see [4]), new integral and series representations are derived here for certain general families of Mathieu type series.

Integral representations and integral transforms of some families of Mathieu type series

2008 ◽  
Vol 19 (7) ◽  
pp. 481-495 ◽  
Author(s):  
Neven Elezović ◽  
H. M. Srivastava ◽  
živorad Tomovski
Keyword(s):  
Integral Transforms ◽  
Integral Representations ◽  
Type Series

scholarly journals On a new (p,q)-Mathieu-type power series and its applications

2019 ◽  
Vol 13 (1) ◽  
pp. 309-324 ◽  
Author(s):  
Khaled Mehrez ◽  
Zivorad Tomovski
Keyword(s):  
Power Series ◽  
Special Function ◽  
Integral Representations ◽  
Type Series ◽  
Type Integral ◽  
Type Power

Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu-type power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of these special function. Moreover, we introduce the notion of the (p, q)-Mittag- Leffler functions and we present a relationships between these two functions. Some other applications are proved, in particular two Tur?n type inequalities for the (p,q)-Mathieu-type series are derived.

THE SOLUTION OF PROBLEMS ON THE COMPUTER: NUMBER, PLOT, SYMBOL

2019 ◽  
pp. 55-63
Author(s):  
V. F. Ochkov ◽  
Yu. V. Chudova ◽  
A. N. Dolgushev
Keyword(s):  
Problem Solving ◽  
Critical Analysis ◽  
Mathematical Constants

The article presents a critical analysis of the methods of analytical, numerical and graphical problem solving on a computer. Problems are solved on the optimal dimensions of hollow geometric bodies (tanks for storing liquids), on the animation of the hinge mechanism, and on the dimensions of the Nautilus submarine. А new set of mathematical constants (numbers and expressions in the radicals), based on the optimization of geometric bodies is presented.

Generalized Kantorovich sampling type series on hypergroups

2018 ◽  
Vol 48 (1) ◽  
pp. 117-127
Author(s):  
Seyyed Mohammad Tabatabaie ◽  
A. Sathish Kumar ◽  
Mahmood Pourgholamhossein
Keyword(s):  
Type Series

First Records of Bufo luchunnicus (Yang et Rao, 2008) and Amolops wenshanensis Yuan, Jin, Li, Stuart et Wu, 2018 (Anura: Bufonidae, Ranidae) from Vietnam

2020 ◽  
Vol 27 (2) ◽  
pp. 81-86
Author(s):  
Cuong The Pham ◽  
Minh Duc Le ◽  
Chung Van Hoang ◽  
Anh Van Pham ◽  
Thomas Ziegler ◽  
...  
Keyword(s):  
Natural History ◽  
Genetic Divergence ◽  
Morphological Data ◽  
Type Series ◽  
Lao Cai ◽  
First Time ◽  
Nd2 Gene ◽  
Quang Ninh

We record two species of amphibians for the first time from Vietnam: Bufo luchunnicus from Lao Cai and Son La provinces and Amolops wenshanensis from Quang Ninh Province. Morphologically, the Vietnamese representatives of B. luchunnicus resemble the type series from China. The specimen of A. wenshanensis from Vietnam slightly differs from the type series from China by having a smaller size (SVL 33.2 mm vs. 35.7 – 39.9 mm in males) and the presence of distinct transverse bands on the dorsal surfaces of limbs. Genetic divergence between the sequence of the Vietnamese specimen and those of A. wenshanensis from China available from GenBank is 1.2 – 1.6% (ND2 gene). In addition, morphological data and natural history notes of aforementioned species are provided from Vietnam.

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