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/*************** -*- Mode: MACSYMA; Package: MAXIMA -*- ******************/
/***************************************************************************
*** *****
*** Copyright (c) 1984 by William Schelter,University of Texas *****
*** All rights reserved *****
***************************************************************************/
kill(all);
done;
deftaylor(f(x),x^2+sum(x^i/(2^i*i!^2),i,4,inf));
[f]$
taylor(%e^sqrt(f(x)),x,0,4);
1+x+x^2/2+3073*x^3/18432+12817*x^4/307200$
niceindices(powerseries(log(sin(x)/x),x,0));
/*('sum((-1)^i1*2^(2*i1)*bern(2*i1)*x^(2*i1)/(i1*(2*i1)!),i1,1,inf))/2$*/
'sum((-1)^i*2^(2*i-1)*bern(2*i)*x^(2*i)/(i*(2*i)!),i,1,inf);
ev(x+sin(3*x)/sin(x),trigexpand,expand);
-sin(x)^2+3*cos(x)^2+x$
trigexpand(sin(10*x+y));
cos(10*x)*sin(y)+sin(10*x)*cos(y)$
-sin(x)^2+3*cos(x)^2+x;
-sin(x)^2+3*cos(x)^2+x$
expand(trigreduce(%));
2*cos(2*x)+x+1$
declare(j,integer,e,even,o,odd);
done$
sin(x+(e+1/2)*%pi),expand;
cos(x)$
sin(x+(o+1/2)*%pi),expand;
-cos(x)$
(linel:500,diff(exp(x^2+y)/(x+y),x,2));
4*x^2*%e^(y+x^2)/(y+x)+2*%e^(y+x^2)/(y+x)-4*x*%e^(y+x^2)/(y+x)^2 +2*%e^(y+x^2)/(y+x)^3$
sconcat(optimize(%));
''(sconcat("block([%1,%2,%3,%4],%1:y+x,%2:x^2,%3:%e^(y+%2),%4:1/%1,4*%2*%4*%3+2*%4*%3-4*x*%3/%1^2+2*%3/%1^3)"))$
linel:79;
79$
laplace(%e^(2*t+a)*sin(t)*t,t,s);
%e^a*(2*s-4)/(s^2-4*s+5)^2$
'integrate(sinh(a*x)*f(t-x),x,0,t)+b*f(t) = t^2;
'integrate(f(t-x)*sinh(a*x),x,0,t)+b*f(t) = t^2$
expand(laplace(%,t,s),0,0);
''(expand(b*laplace(f(t),t,s)+a*laplace(f(t),t,s)/(s^2-a^2) = 2/s^3,0,0))$
linsolve([%],['laplace(f(t),t,s)]);
['laplace(f(t),t,s) = (2*s^2-2*a^2)/(b*s^5+(a-a^2*b)*s^3)]$
(exp : %,0);
0$
assume(a>0,b>0,a*b>1);
[a>0,b>0,a*b>1];
ilt(ev(exp[1]),s,t);
f(t)=-2*cosh(sqrt(a*b*(a*b-1))*t/b)/(a^3*b^2-2*a^2*b+a)+a*t^2/(a*b-1)+2/(a^3*b^2-2*a^2*b+a)$
forget(a>0,b>0,a*b>1);
[a>0,b>0,a*b>1];
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