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Text File  |  2002-05-15  |  1.3 KB  |  43 lines
  1. "File FRESNEL.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
  2.  
  3. DAWSON(x):=-SQRT(pi)*#i*#e^(-x^2)*ERF(#i*x)/2
  4.  
  5. FRESNEL_SIN(z):=INT(SIN(pi*t_^2/2),t_,0,z)
  6.  
  7. FRESNEL_SIN_SERIES(z,m):=SUM(COS(pi*k_)*(pi/2)^(2*k_+1)*z^(4*k_+3)/((2*k_+1)!*~
  8. (4*k_+3)),k_,0,m)
  9.  
  10. FRESNEL_COS(z):=INT(COS(pi*t_^2/2),t_,0,z)
  11.  
  12. FRESNEL_COS_SERIES(z,m):=SUM(COS(pi*k_)*(pi/2)^(2*k_)*z^(4*k_+1)/((2*k_)!*(4*k~
  13. _+1)),k_,0,m)
  14.  
  15. FRESNEL_AUX_F(z):=1/(pi*z)-3/(pi^3*z^5)
  16.  
  17. FRESNEL_AUX_G(z):=1/(pi^2*z^3)-15/(pi^4*z^7)
  18.  
  19. FRESNEL_SIN_ASYMP(z):=1/2-FRESNEL_AUX_F(z)*COS(pi*z^2/2)-FRESNEL_AUX_G(z)*SIN(~
  20. pi*z^2/2)
  21.  
  22. FRESNEL_COS_ASYMP(z):=1/2+FRESNEL_AUX_F(z)*SIN(pi*z^2/2)-FRESNEL_AUX_G(z)*COS(~
  23. pi*z^2/2)
  24.  
  25. SPHERICAL_BESSEL_J2(v):=v/SQRT(SUM((2*k_-1)*v SUB k_^2,k_,1,DIMENSION(v)))
  26.  
  27. SPHERICAL_BESSEL_J1(n,z):=ITERATE(APPEND([(2*(n-DIMENSION(v_))+5)/z*v_ SUB 1-v~
  28. _ SUB 2],v_),v_,[1,0],n)
  29.  
  30. SPHERICAL_BESSEL_J_LIST(n,z):=SPHERICAL_BESSEL_J2(SPHERICAL_BESSEL_J1(n,z))
  31.  
  32. "FRESNEL_SIN_J and FRESNEL_COS_J contributed by Jim FitzSimons."
  33.  
  34. FRESNEL_COS_J_AUX(v,m):=SUM(v SUB (2*k_+1),k_,0,m)
  35.  
  36. FRESNEL_COS_J(z,m):=FRESNEL_COS_J_AUX(z*SPHERICAL_BESSEL_J_LIST(2*m+2,pi*z^2/2~
  37. ),m)
  38.  
  39. FRESNEL_SIN_J_AUX(v,m):=SUM(v SUB (2*k_+2),k_,0,m)
  40.  
  41. FRESNEL_SIN_J(z,m):=FRESNEL_SIN_J_AUX(z*SPHERICAL_BESSEL_J_LIST(2*m+2,pi*z^2/2~
  42. ),m)
  43.