## 1369 Reputation

18 years, 215 days

## openness...

I agree, openness is an asset, though probably it is perceived by Maplesoft as a threat. I hope that that this perception will change.

You could add some comments.to the item, pointing out what is wrong in your opinion. They may help improving it.

## Hypergeometric0F1Regularized(1,0)...

I am not familiar with this Hypergeometric0F1Regularized(1,0) function. Does this MMA expression check right? (i.e. derivative, limit at x=0, etc)

## order of the series...

For choosing a different order of the series expansion, use the environment variable Order. Then you can use convert to get a polynom of the desired degree:

```Order:=11:
dsolve({ode,St(0)=1},St(t),series):
convert(%,polynom);
11   2     11    3      143     4
St(t) = 1 - 1/12 t + ---- t  - ------ t  + --------- t
3456      165888      286654464

2629      5       24013       6         27599        7
+ ------------ t  - -------------- t  + ----------------- t
206391214080      59440669655040      19972065004093440

1245277        8          34830169         9
+ ------------------- t  - ---------------------- t
7669272961571880960      9939377758197157724160

293852581           10
- -------------------------- t
14312703971803907122790400

```

## order of the series...

For choosing a different order of the series expansion, use the environment variable Order. Then you can use convert to get a polynom of the desired degree:

```Order:=11:
dsolve({ode,St(0)=1},St(t),series):
convert(%,polynom);
11   2     11    3      143     4
St(t) = 1 - 1/12 t + ---- t  - ------ t  + --------- t
3456      165888      286654464

2629      5       24013       6         27599        7
+ ------------ t  - -------------- t  + ----------------- t
206391214080      59440669655040      19972065004093440

1245277        8          34830169         9
+ ------------------- t  - ---------------------- t
7669272961571880960      9939377758197157724160

293852581           10
- -------------------------- t
14312703971803907122790400

```

## in Maple 14...

It seems OK, e.g.:

```int(y*exp(-y)*cos(k*y*cos(theta)),  theta= 0..Pi,y = 0..infinity) assuming k>0;
Pi
-----------
2 3/2
(1 + k )

```

## oddities...

Maple 14, with assumptions on x:

```int(BesselK(1,t)*t^2,t=0..x) assuming x>0;
2
-x  BesselK(0, x) - 2 x BesselK(1, x)

+ x BesselK(0, x) BesselI(1, x)

+ x BesselK(1, x) BesselI(0, x)

int(BesselK(1,t)*t^2,t=0..x) assuming x=0;

0

int(BesselK(1,t)*t^2,t=0..x) assuming x<0;

2
2 - x  BesselK(0, x) - 2 x BesselK(1, x)
```

## some history of this bug...

This bug occurs also in Maple 14 and is already observable in Maple 6.02. Maple V R 4.00b does it right:

```F:=int(BesselK(1,t)*t^2,t=0..x);
2
F := -x  BesselK(0, x) - 2 x BesselK(1, x) + 2

limit(F,x=0);

0
```

And Maple V R5.1 produces a series whose coefficients involve Psi functions, and with numerically correct limit.

## No classic...

No, as far as I know. Classic help calls by default the Java browser. And in Classic, helpbrowser can be set to text and get the help page in text form within the Classic worksheet. But, if I execute in Classic

```interface(helpbrowser=classic);
classic

?solve
```

the GUI gets working nonstop. I can interrupt it with the red button though.

And in fact, no Classic help page files are provided.

On the other hand, in Standard GUI, only helpbrowser=standard is possible. I.e. an error occurs here:

```interface(helpbrowser=text);
Error, (in interface) helpbrowser is Read Only
```

(acer offered a hack for that).

## No classic...

No, as far as I know. Classic help calls by default the Java browser. And in Classic, helpbrowser can be set to text and get the help page in text form within the Classic worksheet. But, if I execute in Classic

```interface(helpbrowser=classic);
classic

?solve
```

the GUI gets working nonstop. I can interrupt it with the red button though.

And in fact, no Classic help page files are provided.

On the other hand, in Standard GUI, only helpbrowser=standard is possible. I.e. an error occurs here:

```interface(helpbrowser=text);
Error, (in interface) helpbrowser is Read Only
```

(acer offered a hack for that).

## profile...

In Maple 14 I get:

```f:=y->evalf(Int(x^2/(exp(x)-1), x=y..infinity)):
profile(f):
profile(`evalf/int/IsolateInt`):
`tools/bench`(f(1));
1.438, 35091208

showprofile(alpha);
function           depth    calls     time    time%         bytes   bytes%
---------------------------------------------------------------------------
evalf/int/IsolateInt      1        1    1.422    98.89      34813056    99.21
f                      1        1    0.016     1.11        277576     0.79
---------------------------------------------------------------------------
total:                 2        2    1.438   100.00      35090632   100.00

```

If these numbers are credible, most of the time and bytes are spent in evalf/int/IsolateInt that seems to make some smoothness control.

## profile...

In Maple 14 I get:

```f:=y->evalf(Int(x^2/(exp(x)-1), x=y..infinity)):
profile(f):
profile(`evalf/int/IsolateInt`):
`tools/bench`(f(1));
1.438, 35091208

showprofile(alpha);
function           depth    calls     time    time%         bytes   bytes%
---------------------------------------------------------------------------
evalf/int/IsolateInt      1        1    1.422    98.89      34813056    99.21
f                      1        1    0.016     1.11        277576     0.79
---------------------------------------------------------------------------
total:                 2        2    1.438   100.00      35090632   100.00

```

If these numbers are credible, most of the time and bytes are spent in evalf/int/IsolateInt that seems to make some smoothness control.

## visible...

Both:

```plots[animate](plot3d, [[r,theta,BesselJ(0,2.40483*r)*sin(2*Pi*t)],
r = 0 .. 1, theta = 0 .. 2*Pi, coords = cylindrical], t = 0 .. 1);

plots[animate](plot3d,[[r*cos(theta), r*sin(theta), BesselJ(0,2.40483*r)*
sin(2*Pi*t)], r=0..1, theta=0..2*Pi], t=0..1);
```

work fine for me in Maple 12.02.