| The Poisson Kernel c[0, ¥) | (1-a^2)/((2*p)*(1-2*a*cos[x-b]+a^2)) |
| The Mexican Hat wavelet | (a^(.5))*(2*p-4*p*p*((a*x)^2))*e^(-p*((a*x)^2)) |
| Fourier transform of Mexican Hat | ((1/a)^(.5))*(-4*p*p*((x/a)^2))*e^(-p*((x/a)^2)) |
| The characteristic function c[0, ¥) | ((((x^2)^(1/2)/x)+1)/2) |
| The infinitely differentiable function j(x) = c[0, ¥)e-x-2 |
((((x^2)^(1/2)/x)+1)/2)*exp[-1/x^2] |
| d(x) = 10j(x+1)j(1-x) | 10*(((((x+1)^2)^(1/2)/(x+1))+1)/2)*exp[-1/(x+1)^2]*(((((1-x)^2)^(1/2)/(1-x))+1)/2)*exp[-1/(1-x)^2] |
| da,b(x) = ad(a(x-b)) | a*10*(((((a*(x-b)+1)^2)^(1/2)/(a*(x-b)+1))+1)/2)*exp[-1/(a*(x-b)+1)^2]*(((((1-a*(x-b))^2)^(1/2)/(1-a*(x-b)))+1)/2)*exp[-1/(1-a*(x-b))^2] |