C and Mathematica Programs for Calculation of Lerch's Transcendent

by Sergej V. Aksenov and Ulrich D. Jentschura
v1.0, last updated 1 May 2002

This is the implementation of the combined nonlinear-condensation transformation (CNCT) to calculation of Lerch's transcendent of real arguments.

For more details see Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
S.V. Aksenov, M.A. Savageau, U.D. Jentschura, J. Becher, G. Soff, P.J. Mohr.
Computer Physics Communications, 150, 1--20, 2003.

Source code for the high precision arithmetic library by David M. Bailey that is used by the C++ programs can be downloaded at http://www.nersc.gov/~dhbailey/mpdist/mpdist.html.

Download gzipped tar file lerchphi.tgz.

On many systems, web browsers can download, unzip, and untar these files automatically. On UNIX systems, after downloading the file lerchphi.tgz, the individual files within the zipped tar file can be unbundled by executing the commands tar -zxf lerchphi.tgz.

Alternatively, please follow links to pages from where individual files of the distributions can be downloaded.

Directory tree

lerchphi/

README Instructions on usage.

lerchphi/Documents

lphidoc.pdf User's Guide in PDF format.
lphidoc.tex User's Guide in LaTeX format.

lerchphi/source

lerchphi.c Lerch's transcendent C program in standard double precision.
lerchphimp.cc Lerch's transcendent C++ program in quad-double precision.

lerchphi/Tests

test.c Test driver program for double precision version.
Makefile Makefile to build a test program for double precision version for UNIX systems.
test.out Sample output for double precision version.
testmp.c Test driver program for quad-double precision version.
Makefile.mp Makefile to build a test program for quad-double precision version for UNIX systems.
testmp.linux.cc INTEL-LINUX Test driver program for the quad-double precision version.
Makefile.linux.mp INTEL-LINUX Makefile to build a test program for the quad-double precision version.
testmp.out Sample output for quad-double precision version.
testf77.f Test driver program for calling double precision version from Fortran.
Makefile.f77 Makefile to build a Fortran test program calling double precision version for UNIX systems.
testf77.out Sample output for Fortran program calling double precision version.
MathTest.nb Mathematica notebook that generates reference values for tests.
test.ref Output from the Mathematica notebook that contains reference values for tests.

lerchphi/Mathematica

lerchphi.m Lerch's transcendent Mathematica function.
lerchphidemo.nb Demo notebook for the Lerch's transcendent Mathematica function.

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