# 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/

#### lerchphi/Documents

#### 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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