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java.lang.ObjectnumericalMethods.calculus.specialFunctions.Clausen
A class providing Clausen's integral and Catalans constant. Clausen's integral is the 2π-periodic
function
Cl2(x) = ∑1∞
sin(nx)/ n2
.
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
.
| 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 |
public static final double CATALAN
G.
| Method Detail |
public static double cl2(double x)
Cl2.
- Parameters:
x - a double
- Returns:
Cl2(x)
public static void main(java.lang.String[] args)
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.
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.
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