A Compact Analytical Fit to the Exponential Integral E1(x)

1998 ◽  
Author(s):  
Steven B. Segletes
Keyword(s):  
Exponential Integral

Tables of the Exponential Integral E v (x) = � 1 ∞ e -xu u -v du

1963 ◽  
Vol 47 (360) ◽  
pp. 176
Author(s):  
Alan Fletcher ◽  
Vera I. Pagurova
Keyword(s):  
Exponential Integral

The exponential integral distribution

1987 ◽  
Vol 5 (3) ◽  
pp. 209-211 ◽  
Author(s):  
J.W. Meijer ◽  
N.H.G. Baken
Keyword(s):  
Exponential Integral ◽  
Integral Distribution

Closed-Form Expression for Temperature in a Semi-Infinite Solid Due to a Fast Moving Surface Heat Source

1991 ◽  
Vol 113 (4) ◽  
pp. 828-831 ◽  
Author(s):  
J. A. Tichy
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Frictional Contact ◽  
Closed Form Expression ◽  
Moving Heat Source ◽  
Convolution Integral ◽  
Form Expression ◽  
Exponential Integral ◽  
Surface Conditions ◽  
Closed Form Solutions

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Pe´cle´t number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Pe´cle´t number. Fortunately, the closed-form solutions are accurate at Pe´cle´t number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals Generalizations and applications of Young’s integral inequality by higher order derivatives

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jun-Qing Wang ◽  
Bai-Ni Guo ◽  
Feng Qi
Keyword(s):  
Differential Geometry ◽  
Integral Inequality ◽  
Higher Order ◽  
Integral Inequalities ◽  
List Type ◽  
Definite Integral ◽  
Exponential Integral ◽  
Definite Integrals ◽  
Logarithmic Integral

Abstract In the paper, the authors generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

Analysis of thermal processes: The exponential integral

1972 ◽  
Vol 4 (1) ◽  
pp. 39-45 ◽  
Author(s):  
J. R. Biegen ◽  
A. W. Czanderna
Keyword(s):  
Thermal Processes ◽  
Exponential Integral
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