numericalMethods.calculus.specialFunctions
Class Clausen

java.lang.Object
  |
  +--numericalMethods.calculus.specialFunctions.Clausen

public class Clausen
extends java.lang.Object

A class providing Clausen's integral and Catalans constant. Clausen's integral is the -periodic function

Cl2(x) = ∑1 sin(nx)/ n2 .

Catalan's constant is

G = Cl2(π/2)
  = 1/12 - 1/32 + 1/52 - 1/72 +- …
  = 0.915965594177…

For 0 ≤ x ≤ 2&pi, the following formula (which explains the name "Clausen's integral") holds.

Cl2(x) = - ∫0x log 2sin (ξ/2) dξ

Clausen's integral is almost the same as Milnor's Lobachevski function

Л(x) = - ∫0x log |2 sin (ξ)| dξ = Cl2(2x)/ 2 .

See Also:
"Leonard Lewin. Polylogarithms and Associated Functions. North Holland, New York, 1981."

Field Summary
static double CATALAN
          Catalan's constant G.
 
Method Summary
static double cl2(double x)
          Clausens integral Cl2.
static void main(java.lang.String[] args)
          Prints Chebyshev coefficients to stdout, which are to be pasted into the code.
 
Methods inherited from class java.lang.Object
, clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

CATALAN

public static final double CATALAN
Catalan's constant G.
Method Detail

cl2

public static double cl2(double x)
Clausens integral Cl2.
Parameters:
x - a double
Returns:
Cl2(x)

main

public static void main(java.lang.String[] args)
Prints Chebyshev coefficients to stdout, which are to be pasted into the code. The number of coefficents which are calculated may be passed as argument. The default is 25.
Parameters:
args - a String array. If args.length > 0, then args[0] is expected to have an integer value, which determines the number of coefficients calculated.