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Topic: Clausen function


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  Clausen function - Wikipedia, the free encyclopedia
The Clausen function can also be viewed as a regularization method to give a meaning to the divergent Fourier series:
This regularization technique is similar to zeta function regularization in physics.
A series acceleration for the Clausen function is given by
en.wikipedia.org /wiki/Clausen_function   (293 words)

  
 Clausen - Wikipedia, the free encyclopedia
Jens Clausen (1891 – 1969), a Danish botanist and geneticist
Jørgen Mads Clausen (born 1948), a Danish billionaire
Thomas Clausen (born 1949), a Danish jazz pianist
en.wikipedia.org /wiki/Clausen   (184 words)

  
 GNU Scientific Library -- Reference Manual
If you are writing numerical functions in a program which also uses GSL code you may find it convenient to adopt the same error reporting conventions as in the library.
This function converts the divided-difference representation of a polynomial to a Taylor expansion.
The Airy functions Ai(x) and Bi(x) are defined by the integral representations,
www.gnu.org /software/gsl/manual/gsl-ref.html   (8008 words)

  
 clausen   (Site not responding. Last check: 2007-10-31)
function y = clausen (x) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)).
[y, err] = clausen (...) err contains an estimate of the absolute error in the value y.
This function is from the GNU Scientific Library, see http://www.gnu.org/software/gsl/ for documentation.
octave.sourceforge.net /index/f/clausen.html   (62 words)

  
 GNU Scientific Library -- Reference Manual - Special Functions
The special functions are available in two calling conventions, a natural form which returns the numerical value of the function and an error-handling form which returns an error code.
The Debye functions are defined by the integral D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)).
The transport functions J(n,x) are defined by the integral representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2.
www.math.umn.edu /systems_guide/gsl-1.3/gsl-ref_7.html   (6072 words)

  
 Bibliography
Allasia and R. Besenghi, Numerical calculation of the Riemann zeta function and generalizations by means of the trapezoidal rule, Numerical and Applied Mathematics, Part 2 (Paris 1988) (C. Brezinski, ed.), IMACS Ann.
A portable Fortran subroutine for derivatives of the psi function, ACM Trans.
Coleman, A Fortran subroutine for the Bessel function
math.nist.gov /mcsd/Reports/2001/nesf/node38.html   (8398 words)

  
 Clausen House: Helping People with Developmental Disabilities to Work, Live and Serve in Community Since 1967.
Clausen House: Helping People with Developmental Disabilities to Work, Live and Serve in Community Since 1967.
Our goal is to assist students with increasing their independence, self esteem, and self-expression through meaningful activities which give them a sense of purpose in their lives.
Most of our students function in the mild to moderate range of mental retardation and many are diagnosed with other disabilities.
www.clausenhouse.org /programs/adulted.html   (234 words)

  
 GNU Scientific Library -- Reference Manual - Special Functions (local)   (Site not responding. Last check: 2007-10-31)
The hazard function for the normal distrbution, also known as the inverse Mill's ratio, is defined as h(x) = Z(x)/Q(x) = \sqrt{2/\pi \exp(-x^2 / 2) / \erfc(x/\sqrt 2)}.
This function computes an array of Gegenbauer polynomials C^{(\lambda)}_n(x) for n = 0, 1, 2, \dots, nmax, subject to \lambda > -1/2, nmax >= 0.
This function computes an array of radial eigenfunctions L^{H3d}_l(\lambda, \eta) for 0 <= l <= lmax.
hektor.umcs.lublin.pl /~spectro/gsl-ref_7.html   (6128 words)

  
 Special Functions
These methods compute the Jacobian elliptic functions sn(um), cn(um), dn(um) by descending Landen transformations, and returns the result as an array of 3 elements.
The hazard function for the normal distribution, also known as the inverse Mill's ratio, is defined as h(x) = Z(x)/Q(x) = sqrt{2/pi exp(-x^2 / 2) / erfc(x/sqrt 2)}.
The Conical Functions P^mu_{-(1/2)+i lambda}(x), Q^mu_{-(1/2)+i lambda} are described in Abramowitz and Stegun, Section 8.12.
rb-gsl.rubyforge.org /sf.html   (4190 words)

  
 GNU Scientific Library -- Reference Manual: Clausen Functions   (Site not responding. Last check: 2007-10-31)
The Clausen function is defined by the following integral,
The Clausen functions are declared in the header file
This document was generated by Michael Stenner on February, 14 2002 using
linux.duke.edu /~mstenner/free-docs/gsl-ref-1.0/gsl-ref_73.html   (50 words)

  
 Topcon GTS-220 Series Total Stations
The GTS-220 Series has the internal memory to store up to 8,000 points for data collection, or up to 16,00 points for layout work, Due to this substantial memory capacity, you do not need to worry about memory storage.
TOPCON'S field proven Point Guide function is standard for the GTS-223 / 225 / 226 (GTS-229: Factory Option).
Clausen Instrument Co., Inc. • 5508 Old Wake Forest Rd., Raleigh, NC 27609
www.clausen.net /topcon/totalstation/gts220.html   (459 words)

  
 math   (Site not responding. Last check: 2007-10-31)
Return the log of the beta function of a and b.
The Debye functions are defined by the integral
These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2.
octave.sourceforge.net /index/math.html   (1986 words)

  
 Topcon Auto Levels
Click on the name of a Total Station for more information...
Superior basic function for measuring distance and angle.
Please browse through our site for additional information, or feel free to contact us directly.
www.clausen.net /topcon/totalstation/totalstation.html   (170 words)

  
 CERNLIB - Short writeups
Logarithm of the Gamma Function for Complex Argument
Modified Bessel Functions I and K of Order 1/4, 1/2 and 3/4
Whittaker Function M of Complex Argument and Complex Indices
wwwasdoc.web.cern.ch /wwwasdoc/cernlib.html   (366 words)

  
 Mathematics Archives - Topics in Mathematics - Number Theory
Zeta function, Clausen von Staudt's theorem, asymptotic expansion, bounds and the Euler-Maclaurin formula
Binary Euclid's Algorithm, Chinese Remainder Theorem, Continued fractions, Constructible Numbers, Euler's Function and Congruence Theorem, Farey Series, Formula for Primes, Peano axioms, Pythagorean Triples, Wilson's Theorem
Pseudoprimes Based On The Symmetric Functions Of The Roots Of A Polynomial
archives.math.utk.edu /topics/numberTheory.html   (675 words)

  
 What's New on the Mathematics Archives
The following link was added to the Complex Analysis section of the Math Archives' Topics in Mathematics:
Collection of articles, Dedekind's Problem, Generating Function For Eulerian Numbers, Permutation Loops, Polyomino Enumerations, Powers of Primes Dividing Factorials, The Dartboard Sequence, Binary Games, 414298141056 Quarto Draws Suffice!, Additive and Multiplicative Partitions, Coloring The Edges of an Icosahedron, Cumulative Permutation Sequences, Center of Gravity With Integer Coordinates, and Unification of Eulerians and Binomials, etc.
Tutorial, Introduction to angles, Graphs of the sine and cosine functions, Definition of the trigonometric functions, Trigonometric identities, Right triangle trigonometry, Trigonometric equations
archives.math.utk.edu /whatsnew/mar00.html   (3099 words)

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