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Computing Programs for the Complex Exponential Integral

1960
*
Mathematics of Computation
*

Brief descriptions are also given

doi:10.2307/2003003
fatcat:relc7yzssbhplafqqgw74bbwty
*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. ...##
###
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. ...

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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

2016
*
Proceedings of the 2016 ACM on Multimedia Conference - MM '16
*

Advanced digital holography attracts

doi:10.1145/2964284.2967192
dblp:conf/mm/Chu16
fatcat:lcaazp2pc5emlj24jgh3zycinq
*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. ...##
###
Applications of the Complex Exponential Integral

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] . ...

##
###
Applications of the complex exponential integral

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] . ...

##
###
Analytic evaluation of four-particle integrals with complex parameters

2002
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

The method for analytic evaluation

doi:10.1103/physreva.65.062501
fatcat:yhmnor3qwfha7cyv7ovwcmbf5e
*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*. ...##
###
Tables of 2 π e z 2 � ∞ z e -t 2 dt for Complex z

1960
*
Mathematics of Computation
*

Brief descriptions are also given

doi:10.2307/2003002
fatcat:g57azhe4dnb3tog5gubfb7w2fu
*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. ...##
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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]

2021
*
arXiv
*
pre-print

We present

arXiv:2107.01488v2
fatcat:kxrij6lgb5g5xlh6knbm7a6rje
*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*. ...##
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The Mathematical Tables Project

1944
*
The American mathematical monthly
*

functions

doi:10.1080/00029890.1944.11999159
fatcat:fkx3im342jdblecrz4pjukewzi
*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. ...##
###
Revised Line Profile Function for Hydrogenic Species

2012
*
Open Astronomy
*

as

doi:10.1515/astro-2017-0383
fatcat:eejifhz2bzao5ez4pn4js3u36i
*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*...##
###
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. ...##
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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

1990
*
International Journal of Mathematics and Mathematical Sciences
*

In this study, the double

doi:10.1155/s0161171290000813
fatcat:2bp3o3xiirclvewwtx4uv5ycwu
*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. ...
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