Hi, ROOT experts,
If I were to show people, in a presentation, the equations of pre-defined functions cheb0, cheb1, cheb2, cheb3, …, and cheb9, what would be the equations?
Thank you!
From here you can go to the implementation and find out the following:
// implementation of Chebyshev polynomials using all coefficients
56 // needed for creating TF1 functions
57 inline double Chebyshev0(double , double c0) {
58 return c0;
59 }
60 inline double Chebyshev1(double x, double c0, double c1) {
61 return c0 + c1*x;
62 }
63 inline double Chebyshev2(double x, double c0, double c1, double c2) {
64 return c0 + c1*x + c2*(2.0*x*x - 1.0);
65 }
66 inline double Chebyshev3(double x, double c0, double c1, double c2, double c3) {
67 return c3*Chebyshev::T<3>(x) + Chebyshev2(x,c0,c1,c2);
68 }
69 inline double Chebyshev4(double x, double c0, double c1, double c2, double c3, double c4) {
70 return c4*Chebyshev::T<4>(x) + Chebyshev3(x,c0,c1,c2,c3);
71 }
72 inline double Chebyshev5(double x, double c0, double c1, double c2, double c3, double c4, double c5) {
73 return c5*Chebyshev::T<5>(x) + Chebyshev4(x,c0,c1,c2,c3,c4);
74 }
75 inline double Chebyshev6(double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6) {
76 return c6*Chebyshev::T<6>(x) + Chebyshev5(x,c0,c1,c2,c3,c4,c5);
77 }
78 inline double Chebyshev7(double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7) {
79 return c7*Chebyshev::T<7>(x) + Chebyshev6(x,c0,c1,c2,c3,c4,c5,c6);
80 }
81 inline double Chebyshev8(double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8) {
82 return c8*Chebyshev::T<8>(x) + Chebyshev7(x,c0,c1,c2,c3,c4,c5,c6,c7);
83 }
84 inline double Chebyshev9(double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8, double c9) {
85 return c9*Chebyshev::T<9>(x) + Chebyshev8(x,c0,c1,c2,c3,c4,c5,c6,c7,c8);
86 }
87 inline double Chebyshev10(double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8, double c9, double c10) {
88 return c10*Chebyshev::T<10>(x) + Chebyshev9(x,c0,c1,c2,c3,c4,c5,c6,c7,c8,c9);
89 }