## 571 Reputation

17 years, 216 days
Technical professional in industry or government
Budapest, Hungary

## checking convergence with csum...

Using the command csum (from the Maple Advisor Database by Robert Israel) the convergence of the summation can be checked:

restart;

a := 2/sqrt(n+2)-2/sqrt(n+3);

csum(a,n);

true

## SumTools and _EnvFormal := true...

# in Maple 12:

restart;

with(SumTools):

_EnvFormal := true;

a := 2/sqrt(n+2)-2/sqrt(n+3);

Summation(a, n=1..infinity );

2/3*3^(1/2)

## verify...

You can also check the positivity of a function with the command verify, but it doesn't give you the points where the function is positive.
See below:

restart;
assume(x,'real');
verify(x^2+1,0,'greater_than' ); # it gives true, i.e. the function x^2+1 is positive for every real x.

verify(x^2,0,'greater_than' );  # it gives FAIL: the function x^2 is not everywhere positive (or in another case Maple can not decide it.)

verify(-x^2-1,0,'greater_than' )  ;# it gives false: the function -x^2-1 is everywhere negative.

verify(sin(x),0,'greater_than' ) assuming x>0 and x<Pi;  # it gives true:   sin(x) is positive on the range of (0,Pi).

verify(sin(x),0,'greater_than' ) assuming x>Pi and x<2*Pi; # it gives false:  sin(x) is negative on the range of (Pi,2*Pi)

## algsubs...

Try this:

```F := t -> 1+x(t)^2+t^3 ;
D[1](F)(1);
```
```algsubs(x(1)=-4,algsubs(D(x)(1)=F(1),%));
```

## more assumptions...

Try this:

simplify(sqrt( x^(2*a+2))) assuming x::positive,a::real;

Or without assumpiton with the symbolic keyword:

simplify(sqrt(  x^(2*a+2) ),symbolic);

## some assumption on n?...

I have changed this row in your code to get a simplified formula:

seq(1/Pi*int(f*F(n*x),x=-Pi..Pi),F in [cos,sin]) assuming n::posint

`a0,an,bn := Fouriercoeff(x^2);`

a0, an, bn := 2/3*Pi^2, 4/n^2*(-1)^n, 0

## selectfun...

If y is your expression: var:=op(op(selectfun(y,arctan)));

## e is not reserved for 2.718......

Use exp(1) instead of e: f := x->exp(1)^(-x)*sin(x); plot(f(x),x=0..2*Pi);

## two solutions...

test:=proc(h) unapply(h,x)(1.1) end proc; test(x^3); # Another solution: test:=proc(h) eval(h,op(indets(h))=1.1) end proc; test(t^3);

## with single quotes...

You can try this: restart; f := x[1]+x[1]*x[2]+x[1]*x[2]*x[3]; diff(f, 'x[1]'); int(int(int(f, 'x[1]' = 0 .. 1), 'x[2]' = 0 .. 1), 'x[3]' = 0 .. 1);

## Correct behavior in maple 11....

It is nice to see that my problem can be directly solved in maple 11. Good work!

## It seems to me this bug is fixed in mapl...

It seems to me this bug is fixed in maple 11. Maple 11 gives the full solution. Thanks.

## Maple 11 can calculate it directly....

I am happy to see that maple 11 is definitely stronger than maple 10. I can calculate the mean and the standard deviation of my original expression with maple 11 symbolically.