module definte;
algebraic <<
laplace2_rules :=
{ laplace2(1/~x,~f1,~x) => int(1/x*f1*e^(-s*x),x,0,infinity),
laplace2(1/~x^(~a),~f1,~x) => int(1/x^a*f1*e^(-s*x),x,0,infinity),
laplace2(1/sqrt(~x),~f1,~x)=> int(1/sqrt(x)*f1*e^(-s*x),x,0,infinity),
laplace2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*e^(-s*x),x,0,infinity),
laplace2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*e^(-s*x),x,0,infinity),
laplace2(~x^~a,~f1,~x) => int(x^a*f1*e^(-s*x),x,0,infinity),
laplace2(~x,~f1,~x) => int(x*f1*e^(-s*x),x,0,infinity),
laplace2(sqrt(~x),~f1,~x) => int(sqrt(x)*f1*e^(-s*x),x,0,infinity),
laplace2(sqrt(~x)*~x,~f1,~x)=>int(sqrt(x)*x*f1*e^(-s*x),x,0,infinity),
laplace2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*e^(-s*x),x,0,infinity),
laplace2(~b,~f1,~x) => int(b*f1*e^(-s*x),x,0,infinity),
laplace2(~f1,~x) => int(f1*e^(-s*x),x,0,infinity)
};
let laplace2_rules;
hankel2_rules :=
{ hankel2(1/~x,~f1,~x) =>
int(1/x*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(1/~x^(~a),~f1,~x) =>
int(1/x^a*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(1/sqrt(~x),~f1,~x) =>
int(1/sqrt(x)*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(~x^~a,~f1,~x) =>
int(x^a*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(~x,~f1,~x) => int(x*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(sqrt(~x),~f1,~x) =>
int(sqrt(x)*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(sqrt(~x)*~x,~f1,~x) =>
int(sqrt(x)*x,f1,besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(~b,~f1,~x) => int(b*f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity),
hankel2(~f1,~x) => int(f1*besselj(n,2*(s*x)^(1/2)),x,0,infinity)
};
let hankel2_rules;
Y_transform2_rules :=
{ Y_transform2(1/~x,~f1,~x) =>
int(1/x*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(1/~x^(~a),~f1,~x) =>
int(1/x^a*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(1/sqrt(~x),~f1,~x) =>
int(1/sqrt(x)*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(~x^~a,~f1,~x) =>
int(x^a*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(~x,~f1,~x) =>
int(x*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(sqrt(~x),~f1,~x) =>
int(sqrt(x)*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(sqrt(~x)*~x,~f1,~x) =>
int(sqrt(x)*x*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(~b,~f1,~x) =>
int(b*f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity),
Y_transform2(~f1,~x) => int(f1*bessely(n,2*(s*x)^(1/2)),x,0,infinity)
};
let Y_transform2_rules;
K_transform2_rules :=
{ K_transform2(1/~x,~f1,~x) =>
int(1/x*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(1/~x^(~a),~f1,~x) =>
int(1/x^a*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(1/sqrt(~x),~f1,~x) =>
int(1/sqrt(x)*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(~x^~a,~f1,~x) =>
int(x^a*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(~x,~f1,~x) =>
int(x*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(sqrt(~x),~f1,~x) =>
int(sqrt(x)*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(sqrt(~x)*~x,~f1,~x) =>
int(sqrt(x)*x*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(~b,~f1,~x) =>
int(b*f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity),
K_transform2(~f1,~x) => int(f1*besselK(n,2*(s*x)^(1/2)),x,0,infinity)
};
let K_transform2_rules;
struveh2_rules :=
{ struveh2(1/~x,~f1,~x) =>
int(1/x*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(1/~x^(~a),~f1,~x) =>
int(1/x^a*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(1/sqrt(~x),~f1,~x) =>
int(1/sqrt(x)*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(~x^~a,~f1,~x) =>
int(x^a*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(~x,~f1,~x) =>
int(x*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(sqrt(~x),~f1,~x) =>
int(sqrt(x)*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(sqrt(~x)*~x,~f1,~x) =>
int(sqrt(x)*x*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(~b,~f1,~x) =>
int(b*f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity),
struveh2(~f1,~x) => int(f1*struveh(n,2*(s*x)^(1/2)),x,0,infinity)
};
let struveh2_rules;
fourier_sin2_rules :=
{ fourier_sin2(1/~x,~f1,~x) => int(1/x*f1*sin(s*x),x,0,infinity),
fourier_sin2(1/~x^(~a),~f1,~x) => int(1/x^a*f1*sin(s*x),x,0,infinity),
fourier_sin2(1/sqrt(~x),~f1,~x) =>
int(1/sqrt(x)*f1*sin(s*x),x,0,infinity),
fourier_sin2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*sin(s*x),x,0,infinity),
fourier_sin2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*sin(s*x),x,0,infinity),
fourier_sin2(~x^~a,~f1,~x) => int(x^a*f1*sin(s*x),x,0,infinity),
fourier_sin2(~x,~f1,~x) => int(x*f1*sin(s*x),x,0,infinity),
fourier_sin2(sqrt(~x),~f1,~x)=> int(sqrt(x)*f1*sin(s*x),x,0,infinity),
fourier_sin2(sqrt(~x)*~x,~f1,~x) =>
int(sqrt(x)*x*f1*sin(s*x),x,0,infinity),
fourier_sin2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*sin(s*x),x,0,infinity),
fourier_sin2(~b,~f1,~x) => int(b*f1*sin(s*x),x,0,infinity),
fourier_sin2(~f1,~x) => int(f1*sin(s*x),x,0,infinity)
};
let fourier_sin2_rules;
fourier_cos2_rules :=
{ fourier_cos2(1/~x,~f1,~x) => int(1/x*f1*cos(s*x),x,0,infinity),
fourier_cos2(1/~x^(~a),~f1,~x) => int(1/x^a*f1*cos(s*x),x,0,infinity),
fourier_cos2(1/sqrt(~x),~f1,~x) =>
int(1/sqrt(x)*f1*cos(s*x),x,0,infinity),
fourier_cos2(1/(sqrt(~x)*~x),~f1,~x) =>
int(1/(sqrt(x)*x)*f1*cos(s*x),x,0,infinity),
fourier_cos2(1/(sqrt(~x)*~x^~a),~f1,~x) =>
int(1/(sqrt(x)*x^a)*f1*cos(s*x),x,0,infinity),
fourier_cos2(~x^~a,~f1,~x) => int(x^a*f1*cos(s*x),x,0,infinity),
fourier_cos2(~x,~f1,~x) => int(x*f1*cos(s*x),x,0,infinity),
fourier_cos2(sqrt(~x),~f1,~x)=> int(sqrt(x)*f1*cos(s*x),x,0,infinity),
fourier_cos2(sqrt(~x)*~x,~f1,~x) =>
int(sqrt(x)*x*f1*cos(s*x),x,0,infinity),
fourier_cos2(sqrt(~x)*~x^~a,~f1,~x) =>
int(sqrt(x)*x^a*f1*cos(s*x),x,0,infinity),
fourier_cos2(~b,~f1,~x) => int(b*f1*cos(s*x),x,0,infinity),
fourier_cos2(~f1,~x) => int(f1*cos(s*x),x,0,infinity)
};
let fourier_cos2_rules;
>>;
endmodule;
end;