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KelvinFunctions.h
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1 // @(#)root/mathmore:$Id$
2 
3 // CodeCogs GNU General Public License Agreement
4 // Copyright (C) 2004-2005 CodeCogs, Zyba Ltd, Broadwood, Holford, TA5 1DU,
5 // England.
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21 
22 #ifndef ROOT_Math_KelvinFunctions
23 #define ROOT_Math_KelvinFunctions
24 
25 //////////////////////////////////////////////////////////////////////////
26 // //
27 // KelvinFunctions //
28 // //
29 // Calculates the Kelvin Functions Ber(x), Bei(x), Ker(x), Kei(x), and //
30 // their first derivatives. //
31 // //
32 //////////////////////////////////////////////////////////////////////////
33 
34 
35 namespace ROOT {
36 namespace Math {
37 
39 {
40  public:
41  // The Kelvin functions and their first derivatives
42  static double Ber(double x);
43  static double Bei(double x);
44  static double Ker(double x);
45  static double Kei(double x);
46  static double DBer(double x);
47  static double DBei(double x);
48  static double DKer(double x);
49  static double DKei(double x);
50 
51  // Utility functions appearing in the calculations of the Kelvin
52  // functions.
53  static double F1(double x);
54  static double F2(double x);
55  static double G1(double x);
56  static double G2(double x);
57  static double M(double x);
58  static double Theta(double x);
59  static double N(double x);
60  static double Phi(double x);
61 
62  // Include and empty virtual desctructor to eliminate compiler warnings
63  virtual ~KelvinFunctions() {}
64 
65  protected:
66  // Internal parameters used to control calculation method and convegence
67  static double fgMin;
68  static double fgEpsilon;
69 
70 };
71 
72 } // namespace Math
73 } // namespace ROOT
74 
75 
76 #endif
77 
static double Ber(double x)
Begin_Latex Ber(x) = Ber_{0}(x) = Re::left[J_{0}#left(x e^{3#pii/4}#right)#right] End_Latex where x i...
static double DBei(double x)
Calculates the first derivative of Bei(x).
static double F1(double x)
Utility function appearing in the calculations of the Kelvin functions Bei(x) and Ber(x) (and their d...
Double_t x[n]
Definition: legend1.C:17
static double G1(double x)
Utility function appearing in the calculations of the Kelvin functions Bei(x) and Ber(x) (and their d...
static double Kei(double x)
Begin_Latex Kei(x) = Kei_{0}(x) = Im::left[K_{0}#left(x e^{3#pii/4}#right)#right] End_Latex where x i...
static double DKer(double x)
Calculates the first derivative of Ker(x).
static double M(double x)
Utility function appearing in the asymptotic expansions of DBer(x) and DBei(x).
static double Bei(double x)
Begin_Latex Bei(x) = Bei_{0}(x) = Im::left[J_{0}#left(x e^{3#pii/4}#right)#right] End_Latex where x i...
static double Theta(double x)
Utility function appearing in the asymptotic expansions of DBer(x) and DBei(x).
static double G2(double x)
Utility function appearing in the calculations of the Kelvin functions Kei(x) and Ker(x) (and their d...
static double DBer(double x)
Calculates the first derivative of Ber(x).
static double Phi(double x)
Utility function appearing in the asymptotic expansions of DKer(x) and DKei(x).
static double Ker(double x)
Begin_Latex Ker(x) = Ker_{0}(x) = Re::left[K_{0}#left(x e^{3#pii/4}#right)#right] End_Latex where x i...
static double DKei(double x)
Calculates the first derivative of Kei(x).
static double F2(double x)
Utility function appearing in the calculations of the Kelvin functions Kei(x) and Ker(x) (and their d...
static double N(double x)
Utility function appearing in the asymptotic expansions of DKer(x) and DKei(x).