Recovering a function from its trigonometric integral

2010 ◽  
Vol 201 (7) ◽  
pp. 1053-1068
Author(s):  
Tat'yana A Sworowska
Keyword(s):  
Trigonometric Integral

scholarly journals Simultaneous Contour Method of a Trigonometric Integral by Prudnikov et al.

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1453
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Contour Method ◽  
Substantial Part ◽  
Exponential Functions ◽  
Closed Form Solutions ◽  
Definite Integrals ◽  
Transcendental Functions ◽  
Trigonometric Integral

In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new.

Triple trigonometric integral equations with an application

1980 ◽  
Vol 10 (2) ◽  
pp. 83-92 ◽  
Author(s):  
Brij M. Singh ◽  
Ranjit S. Dhaliwalt ◽  
I. N. Sneddon
Keyword(s):  
Integral Equations ◽  
Trigonometric Integral

Trigonometric integral

1979 ◽  
Vol 14 (6) ◽  
pp. 332-332 ◽  
Author(s):  
O S Heavens ◽  
D F A Edwards
Keyword(s):  
Trigonometric Integral

scholarly journals An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions

10.37236/1528 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Lane Clark
Keyword(s):  
Asymptotic Expansion ◽  
Complete Asymptotic Expansion ◽  
Trigonometric Integral

Let $b(n,k)$ denote the number of permutations of $\{1,\ldots,n\}$ with precisely $k$ inversions. We represent $b(n,k)$ as a real trigonometric integral and then use the method of Laplace to give a complete asymptotic expansion of the integral. Among the consequences, we have a complete asymptotic expansion for $b(n,k)/n!$ for a range of $k$ including the maximum of the $b(n,k)/n!$.

Evaluation of a Trigonometric Integral

1947 ◽  
Vol 54 (4) ◽  
pp. 221
Author(s):  
J. P. Hoyt
Keyword(s):  
Trigonometric Integral
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