Wolfgang Yourgrau and Donald Livingstone. On the matter of mathematical constants. Methodos, vol. 9 (1957), pp. 3–29.

1966 ◽  
Vol 31 (1) ◽  
pp. 115-115
Author(s):  
H. Arnold Schmidt
Keyword(s):  
Mathematical Constants

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.

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.

Mathematical constants

2004 ◽  
Vol 41 (11) ◽  
pp. 41-6581-41-6581
Keyword(s):  
Mathematical Constants

scholarly journals MATHEMATICAL CONSTANTS.

1971 ◽  
Author(s):  
H.P. Robinson ◽  
Elinor Potter
Keyword(s):  
Mathematical Constants

scholarly journals Definite Integral of Arctangent and Polylogarithmic Functions Expressed as a Series

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1099 ◽  
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Special Functions ◽  
Contour Integration ◽  
Definite Integral ◽  
Catalan’S Constant ◽  
Infinite Sums ◽  
Mathematical Constants

We present a method using contour integration to evaluate the definite integral of arctangent reciprocal logarithmic integrals in terms of infinite sums. In a similar manner, we evaluate the definite integral involving the polylogarithmic function L i k ( y ) in terms of special functions. In various cases, these generalizations give the value of known mathematical constants such as Catalan’s constant G, Aprey’s constant ζ ( 3 ) , the Glaisher–Kinkelin constant A, l o g ( 2 ) , and π .

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