49g+ Summation help
BobLogan
When I EVAL the simple sum E(X=1,6,1/(X+1)), I would like to get a number,
but instead I get -(Psi(2)-Psi(8)). What is going on? I would really like
to be able to do sums on my calc, but the answer it is giving me is
useless. Please help!
Bob
Bhuvanesh
If I recall correctly, the 49G doesn't really support the polygamma
function (Psi), so you're at a dead end unless:
* You simply enumerate the terms and sum them, or
* You find a third-party polygamma function implementation
Bhuvanesh.
Gene
Gene: Hi Bob. My guess is that if you check your MODES then CAS
settings, you don't have a checkmark in the "Numeric" box.
When I do your sum in the Equationwriter without a checkmark in the
Numeric field, I get the "psi" function thing you report.
When numeric is checked, I get a numeric answer of 1.5928 something.
Virgil
"Gene" <gene....@gmail.com> wrote:
After which XQ or\->Q or \->Q\pi will give the correct '223/140'
fraction form.
Once you get the decimal form, XQ or\->Q or \->Q\pi will give the right
rational form up to E(X=1,11,1/(X+1))
Alternately, enter your values as reals, even in exact mode, so that
you have 'E(X=1.,6.,1./(X+1.))' instead of 'E(X=1,6,1/(X+1))'
and you will get the decimal result instead of the symbolic one.
If you have to have exact rational forms, the summation function won't
do it. You would have to do it with some sort of loop in exact mode,
e.g.:
\<< 0 1 6 FOR X X 1 + INV + EVAL NEXT \>>
More generally, putting the lower limit and upper limit on the stack in
levels 2 and 1 respectively and executing
\<< 0 UNROT FOR X X 1 + INV + EVAL NEXT \>> will give the correct value
in fraction form up to the limit of the exact mode.
BobLogan
I played around with the summation function for a while and it looks like
it only returns the Psi when there's an INV in the function. For example,
E(X=1,6,(X+7)^2) gave me the answer I expected (an integer). However, I
was surprised to see that E(X=1,6,(SIN(X)+7)^2)) returned 295.68 even
though I had the exact and symbolic modes on.
The inconsistency in the answers is quite annoying. I'll probably make my
own summation program sometime.
Bob
VPN
news:1109981713.6...@f14g2000cwb.googlegroups.com...
> BobLogan wrote:
>> When I EVAL the simple sum E(X=1,6,1/(X+1)), I would like to get a
> number,
>> but instead I get -(Psi(2)-Psi(8)). What is going on? I would really
> like
>> to be able to do sums on my calc, but the answer it is giving me is
>> useless. Please help!
>
> If I recall correctly, the 49G doesn't really support the polygamma
> function (Psi), so you're at a dead end unless:
Have you tried PSI/Psi?
The non-supported pseudo functions appear inside a
(I)LAP Command Algebraic: Heaviside and Delta
All functions in the CATalog can give numeric answers
There are some analytic functions missing, like
(A)SEC(H), (A)CSC(H), (A)COT(H),
Also there is no support for some common integrals
ans special functions, but what do you expect on a CAS
with so little ROM/RAM?
What did you mean, Bhuv?
[VPN]
acl
What's strange is that the relation between the digamma and polygamma
functions isn't implemented (one is the nth derivative of the other);
this should have been easy to do, and can be done by defining d1Psi as
<< -> x 'PSI(x,1)' >> and so on. Then, Psi(X) DERVX gives d1PSI(X);
EVAL gives PSI(X,1). Then {X 4} | followed by EVAL gives -49/36+
pi^2/6, which is correct. In fact, after a few minutes of testing, it
looks like most of the explicit expressions for eg Psi(n,x) are given
by the calculator except for the ones involving Euler's constant.
OK, if I remember correctly, Psi(n) where n is an integer is of the
form
n1/n2-gamma
where gamma is Euler's constant and n1,n2 integers; this means that
Psi(m1)-Psi(m2) has also a rational form (obvious from the initial
summation anyway), ie the gammas cancel out. The only problem is that
the calculator's CAS doesn't give explicit expressions for the Psi(m)
(as mentioned above) and so never discovers that the gammas cancel...
"Bhuvanesh" <lalu_...@yahoo.com> wrote in message news:<1109981713.6...@f14g2000cwb.googlegroups.com>...
Bhuvanesh
VPN wrote:
> "Bhuvanesh" <lalu_...@yahoo.com> wrote:
> > If I recall correctly, the 49G doesn't really support the polygamma
> > function (Psi), so you're at a dead end unless:
>
> Have you tried PSI/Psi?
No, I should have :-) Apparently one can numericize results involving
Psi.
> There are some analytic functions missing, like
> (A)SEC(H), (A)CSC(H), (A)COT(H),
This is not a big deal in my opinion. Are these used widely in Europe?
> Also there is no support for some common integrals
> ans special functions, but what do you expect on a CAS
> with so little ROM/RAM?
Well, we [power-users] always expect more than what is realistic, don't
we? ;-)
Thanks for the correction.
Regards,
Bhuvanesh.