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Computing Programs for the Complex Exponential Integral

J. W. W., A. V. Hershey
1960 Mathematics of Computation  
Brief descriptions are also given of two NORC subroutines for the calculation of the exponential integral and the sine and cosine integrals of a real argument.  ...  Hersney, Computing Programs for the Complex Exponential Integral, NAVORD Report No. 5909, NPG Report No. 1646, U. S. Naval Proving Ground, Dablgren, Virginia, June 1959, iii + 16 p.  ... 
doi:10.2307/2003003 fatcat:relc7yzssbhplafqqgw74bbwty

Page 6374 of Mathematical Reviews Vol. , Issue 92k [page]

1992 Mathematical Reviews  
of a complex argument.  ...  These results are useful for curve design.” 92k:65025 65D20 Amos, Donald E. (1-SAND) Computation of exponential integrals of a complex argument. ACM Trans. Math. Software 16 (1990), no. 2, 169-177.  ... 

Page 89 of Mathematics of Computation Vol. 8, Issue 46 [page]

1954 Mathematics of Computation  
The present table is therefore concerned with the exponential integral for complex argument, not the generalized exponential-integral which has been tabulated by the Harvard University Computation Laboratory  ...  Spotchecking a few values against the forthcoming NBS Tables of Exponential Integrals for Complex Arguments (cartesian form) did not reveal any discrepancy.  ... 

Efficient Digital Holographic Image Reconstruction on Mobile Devices

Chung-Hua Chu
2016 Proceedings of the 2016 ACM on Multimedia Conference - MM '16  
Advanced digital holography attracts a lot of attentions for 3D visualization nowadays.  ...  To reduce computational complexity in digital holographic image reconstruction, we propose an efficient and effective algorithm to simplify Fresnel transforms for the mobile devices.  ...  Since the argument of the exponential function is a complex number, we transform   into () + () where  is equal to √ −1.  ... 
doi:10.1145/2964284.2967192 dblp:conf/mm/Chu16 fatcat:lcaazp2pc5emlj24jgh3zycinq

Applications of the Complex Exponential Integral

Murlan S. Corrington
1961 Mathematics of Computation  
Computer routines for the complex exponential integral are also available [6] . 6 .  ...  Tables of sine and cosine integrals for complex arguments in rectangular coordinates have been published by Bleick [4] .  ... 
doi:10.2307/2003084 fatcat:l3rwgldwbnd5fmo6xah3eupbm4

Applications of the complex exponential integral

Murlan S. Corrington
1961 Mathematics of Computation  
Computer routines for the complex exponential integral are also available [6] . 6 .  ...  Tables of sine and cosine integrals for complex arguments in rectangular coordinates have been published by Bleick [4] .  ... 
doi:10.1090/s0025-5718-1961-0124536-x fatcat:5dda5zz6arfg7jzk35ihwbdjwy

Analytic evaluation of four-particle integrals with complex parameters

V. S. Zotev, T. K. Rebane
2002 Physical Review A. Atomic, Molecular, and Optical Physics  
The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters.  ...  It allows high precision variational solution of the Coulomb four-body problem in a basis of exponential-trigonometric functions of interparticle separations.  ...  This method reduces computation of integrals, needed to determine matrix elements of a four-particle Hamiltonian, to evaluation of the dilogarithmic function [5] of various arguments.  ... 
doi:10.1103/physreva.65.062501 fatcat:yhmnor3qwfha7cyv7ovwcmbf5e

Tables of 2 π e z 2 � ∞ z e -t 2 dt for Complex z

R. Hensman, D. P. Jenkins
1960 Mathematics of Computation  
Brief descriptions are also given of two NORC subroutines for the calculation of the exponential integral and the sine and cosine integrals of a real argument.  ...  Hersney, Computing Programs for the Complex Exponential Integral, NAVORD Report No. 5909, NPG Report No. 1646, U. S. Naval Proving Ground, Dablgren, Virginia, June 1959, iii + 16 p.  ... 
doi:10.2307/2003002 fatcat:g57azhe4dnb3tog5gubfb7w2fu

Page 261 of Mathematics of Computation Vol. 5, Issue 36 [page]

1951 Mathematics of Computation  
Error Functions of a Complex Variable 67-70 Euclid’s Algorithm 133 Exponential Function 7, 27, 70, 190-191, 200 Exponential Integral 55, 156, 162-167, 184, 202 Exponential Integral, Complex Argument 202  ...  , Incomplete 156, 221 Gamma Function, Log of 203 Gamma Function, Reciprocal of 160-161 Gear Ratios 138 261 General Electric Computers 95 Geodetic Tables 26-27, 187, 198, 212 Graphs 49 Hankel Functions  ... 

A fast algorithm for computing the Boys function [article]

Gregory Beylkin, Sandeep Sharma
2021 arXiv   pre-print
We present a new fast algorithm for computing the Boys function using a nonlinear approximation of the integrand via exponentials.  ...  The resulting algorithms evaluate the Boys function with real and complex valued arguments and are competitive with previously developed algorithms for the same purpose.  ...  for computing the error function of complex argument.  ... 
arXiv:2107.01488v2 fatcat:kxrij6lgb5g5xlh6knbm7a6rje

The Mathematical Tables Project

1944 The American mathematical monthly  
functions of fractional order, Bessel functions of the second kind for complex arguments, exponential integrals for complex arguments, and Chebyschev polynomials.  ...  Since its founding, the Project has done an amazing amount of work, em- ploying at times a huge corps of computers and computing machines, working in two shifts. Professor A. N.  ... 
doi:10.1080/00029890.1944.11999159 fatcat:fkx3im342jdblecrz4pjukewzi

Revised Line Profile Function for Hydrogenic Species

A. Sapar, R. Poolamäe
2012 Open Astronomy  
as a new argument.  ...  AbstractAnalytical series expansions for the hydrogenic spectral line profile functions are derived starting from the three single expressions, obtained by integrating twice the convolution of the Holtsmark  ...  expansions of the exponential function ε(x), it is useful to introduce a complex phase factor for β in the needed integrals K j (β) = ∞ ∫ 0 x j exp(iβx)ε(x)dx = c j (β) + is j (β), (14) where the complex  ... 
doi:10.1515/astro-2017-0383 fatcat:eejifhz2bzao5ez4pn4js3u36i

Page 1672 of Mathematical Reviews Vol. 57, Issue 5 [page]

1979 Mathematical Reviews  
E. 57 #12870 Distribution of values of entire functions of a discrete complex argument that depend on a continuous real argument. (Russian) Taskent. Gos. Univ. Nauén.  ...  A.; HuSvaktov, 5. D.; 57 #12868 Cumakoy, S. A. Analytic functions of a discrete complex argument on invariant lattices. (Russian) Taskent. Gos. Univ. Naucn.  ... 

Page 540 of The American Mathematical Monthly Vol. 51, Issue 9 [page]

1944 The American Mathematical Monthly  
functions of fractional order, Bessel functions of the second kind for complex arguments, exponential integrals for complex arguments, and Chebyschev polynomials.  ...  Since its founding, the Project has done an amazing amount of work, em- ploying at times a huge corps of computers and computing machines, working in two shifts. Professor A. N.  ... 

Three dimensional Green's function for ship motion at forward speed

Matiur Rahman
1990 International Journal of Mathematics and Mathematical Sciences  
In this study, the double integrals have been replaced by single integrals with the use of complex exponential integrals.  ...  It has been found that this analysis provides an efficient way of computing the wave resistance for three dimensional potential problem of ship motion with forward speed.  ...  OSC87-00549-(010) with the Defence Research Establishment Atlantic while the author was on Sabbatical Leave from the Technical University of Nova Scotia.  ... 
doi:10.1155/s0161171290000813 fatcat:2bp3o3xiirclvewwtx4uv5ycwu
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