Robert M. Corless
Department of Applied Mathematics
University of Western Ontario
London, Canada

Copyright 2001 by Robert M. Corless
All rights reserved

Useful one-word commands 

Использование монокоманд

Manipulations from calculus 

Манипуляции из начал анализа

series

Команда series

> restart;
> series( sin(x), x, 13 );

series(1*x-1/6*x^3+1/120*x^5-1/5040*x^7+1/362880*x^...
> series( x^x, x, 5 );

series(1+ln(x)*x+1/2*ln(x)^2*x^2+1/6*ln(x)^3*x^3+1/...
> asympt(1/GAMMA(x), x, 3 );

(1/2*2^(1/2)/Pi^(1/2)/(1/x)^(1/2)-1/24*2^(1/2)/Pi^(...
> series( sin(x)^(1/3), x );

x^(1/3)-1/18*x^(7/3)-1/3240*x^(13/3)+O(x^(19/3))
> alias(alpha=RootOf(z^3+z+1, z));

alpha
> series(RootOf(z^3+(1+x)*z+1, z), x);

> x = t*tan(t);

x = t*tan(t)
> map(series, %, t=Pi/4 );

> solve( %, t );

> restart;
> f := ( sin(tan(x)) - tan(sin(x)) )/x^7;

f := (sin(tan(x))-tan(sin(x)))/x^7
> series( f, x );

series(O(x^(-1)),x,-1)
> for k to 5 do Order := Order + 1; series( f , x ); end do;
Order := 7
series(O(1),x,0)
Order := 8
series(-1/30+O(x),x,1)
Order := 9
series(-1/30+O(x^2),x,2)
Order := 10
series(-1/30-29/756*x^2+O(x^3),x,3)
Order := 11
series(-1/30-29/756*x^2+O(x^4),x,4)

С официального разрешения                    © 2002 Waterloo Maple, Inc