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- "File FRESNEL.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
-
- DAWSON(x):=-SQRT(pi)*#i*#e^(-x^2)*ERF(#i*x)/2
-
- FRESNEL_SIN(z):=INT(SIN(pi*t_^2/2),t_,0,z)
-
- FRESNEL_SIN_SERIES(z,m):=SUM(COS(pi*k_)*(pi/2)^(2*k_+1)*z^(4*k_+3)/((2*k_+1)!*~
- (4*k_+3)),k_,0,m)
-
- FRESNEL_COS(z):=INT(COS(pi*t_^2/2),t_,0,z)
-
- FRESNEL_COS_SERIES(z,m):=SUM(COS(pi*k_)*(pi/2)^(2*k_)*z^(4*k_+1)/((2*k_)!*(4*k~
- _+1)),k_,0,m)
-
- FRESNEL_AUX_F(z):=1/(pi*z)-3/(pi^3*z^5)
-
- FRESNEL_AUX_G(z):=1/(pi^2*z^3)-15/(pi^4*z^7)
-
- FRESNEL_SIN_ASYMP(z):=1/2-FRESNEL_AUX_F(z)*COS(pi*z^2/2)-FRESNEL_AUX_G(z)*SIN(~
- pi*z^2/2)
-
- FRESNEL_COS_ASYMP(z):=1/2+FRESNEL_AUX_F(z)*SIN(pi*z^2/2)-FRESNEL_AUX_G(z)*COS(~
- pi*z^2/2)
-
- SPHERICAL_BESSEL_J2(v):=v/SQRT(SUM((2*k_-1)*v SUB k_^2,k_,1,DIMENSION(v)))
-
- SPHERICAL_BESSEL_J1(n,z):=ITERATE(APPEND([(2*(n-DIMENSION(v_))+5)/z*v_ SUB 1-v~
- _ SUB 2],v_),v_,[1,0],n)
-
- SPHERICAL_BESSEL_J_LIST(n,z):=SPHERICAL_BESSEL_J2(SPHERICAL_BESSEL_J1(n,z))
-
- "FRESNEL_SIN_J and FRESNEL_COS_J contributed by Jim FitzSimons."
-
- FRESNEL_COS_J_AUX(v,m):=SUM(v SUB (2*k_+1),k_,0,m)
-
- FRESNEL_COS_J(z,m):=FRESNEL_COS_J_AUX(z*SPHERICAL_BESSEL_J_LIST(2*m+2,pi*z^2/2~
- ),m)
-
- FRESNEL_SIN_J_AUX(v,m):=SUM(v SUB (2*k_+2),k_,0,m)
-
- FRESNEL_SIN_J(z,m):=FRESNEL_SIN_J_AUX(z*SPHERICAL_BESSEL_J_LIST(2*m+2,pi*z^2/2~
- ),m)