Math Is Fun Forum

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: What do you think?

It didn't.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: What do you think?

hi bobbym

look at post #1150.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi;

I will look at it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Last edited by gAr (2011-06-27 16:07:03)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

The limit of that is infinity. Perhaps an easier way to determine the constant term is to change the diophantine equation a little.

Make the substitution:

Now the diophantine equation is

Meaning we check the coefficient of x^100. It should be easier to get a general form for this coefficient.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

I get:

?

Last edited by gAr (2011-06-27 21:22:08)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

That formula will only work for:

when

But this one is:

There are less solutions.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Ah, yes!
So no closed form?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

That is a really good question. I do not know the answer to it.

It seems I unwisely constructed the problem to have constraints that were less than the coefficient of the power of x I needed. This does make it harder to find a closed form for the coefficients.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Okay. I thought you had a closed form when you asked for an easier way.
For a computer, both are easy!

Anyway, that limit is still bugging me:

How to expand the reciprocal terms?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi;

Not every function has a Mclaurin expansion. That function is undefined at 0.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi,

Then how does a CAS expand it at 0?!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi;

You are right. Mine is even getting the 84451. Weird!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Maybe it checks for the common factors before expanding?

If it can be expanded like that, limit must exist here also, isn't it?

Last edited by gAr (2011-06-27 22:22:39)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

It is the way you are representing it that might be the problem.

This way has no problems with divide by zero.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

I'm still getting ∞ for that, both in wolframalpha and sage!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi;

Me too. It is very strange. I have no explanation for it right now.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

I'm also unable to get anything.
I doubt that the algebra systems are simply multiplying polynomials instead of taylor expansion.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi;

Some thoughts on this:

For one thing when you ask a package for a series representation that does not mean it used a Taylor series to get it.

Second in an ordinary generating function the constant term is found when x = 0. But in this one the constant term is generated by cancellations between x^n and x^(-n). It is no wonder that we can not find f(0). It would not give the correct answer anyway.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi,

Yes, that's right.
In sage, I specified taylor expansion, so I was surprised.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

When they have negative powers they are called Laurent series.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: What do you think?

hi all

tried to get the derivative of the function above and got this in an online limit calculator:
(100*x^200+396*x^199+980*x^198+1940*x^197+3360*x^196+5320*x^195+7896*x^194+11160*x^193+
15180*x^192+20020*x^191+25740*x^190+32396*x^189+40040*x^188+48720*x^187+58480*x^186+
69360*x^185+81396*x^184+94620*x^183+109060*x^182+124740*x^181+141680*x^180+159896*x^179+
179400*x^178+200200*x^177+222300*x^176+245700*x^175+270396*x^174+296380*x^173+323640*
x^172+352160*x^171+381920*x^170+412896*x^169+445060*x^168+478380*x^167+512820*x^166+
548340*x^165+584896*x^164+622440*x^163+660920*x^162+700280*x^161+740460*x^160+781396*
x^159+823020*x^158+865260*x^157+908040*x^156+951280*x^155+994896*x^154+1038800*x^153+
1082900*x^152+1127100*x^151+1171300*x^150+1215200*x^149+1258512*x^148+1300960*x^147+
1342280*x^146+1382220*x^145+1420540*x^144+1457012*x^143+1491420*x^142+1523560*x^141+
1553240*x^140+1580280*x^139+1604512*x^138+1625780*x^137+1643940*x^136+1658860*x^135+
1670420*x^134+1678512*x^133+1683040*x^132+1683920*x^131+1681080*x^130+1674460*x^129+
1664012*x^128+1649700*x^127+1631500*x^126+1609400*x^125+1583400*x^124+1553512*x^123+
1519760*x^122+1482180*x^121+1440820*x^120+1395740*x^119+1347012*x^118+1294720*x^117+
1238960*x^116+1179840*x^115+1117480*x^114+1052012*x^113+983580*x^112+912340*x^111+
838460*x^110+762120*x^109+683512*x^108+602840*x^107+520320*x^106+436180*x^105+350660*
x^104+264012*x^103+176500*x^102+88400*x^101-88400*x^99-176500*x^98-264012*x^97-350660*
x^96-436180*x^95-520320*x^94-602840*x^93-683512*x^92-762120*x^91-838460*x^90-912340*
x^89-983580*x^88-1052012*x^87-1117480*x^86-1179840*x^85-1238960*x^84-1294720*x^83-
1347012*x^82-1395740*x^81-1440820*x^80-1482180*x^79-1519760*x^78-1553512*x^77-1583400*
x^76-1609400*x^75-1631500*x^74-1649700*x^73-1664012*x^72-1674460*x^71-1681080*x^70-1683920*x^69-1683040*x^68-1678512*x^67-1670420*x^66-1658860*x^65-1643940*x^64-1625780*
x^63-1604512*x^62-1580280*x^61-1553240*x^60-1523560*x^59-1491420*x^58-1457012*x^57-1420540*x^56-1382220*x^55-1342280*x^54-1300960*x^53-1258512*x^52-1215200*x^51-1171300*
x^50-1127100*x^49-1082900*x^48-1038800*x^47-994896*x^46-951280*x^45-908040*x^44-865260*
x^43-823020*x^42-781396*x^41-740460*x^40-700280*x^39-660920*x^38-622440*x^37-584896*
x^36-548340*x^35-512820*x^34-478380*x^33-445060*x^32-412896*x^31-381920*x^30-352160*
x^29-323640*x^28-296380*x^27-270396*x^26-245700*x^25-222300*x^24-200200*x^23-179400*
x^22-159896*x^21-141680*x^20-124740*x^19-109060*x^18-94620*x^17-81396*x^16-69360*x^15-
58480*x^14-48720*x^13-40040*x^12-32396*x^11-25740*x^10-20020*x^9-15180*x^8-11160*x^7-7896*
x^6-5320*x^5-3360*x^4-1940*x^3-980*x^2-396*x-100)/x^101

Last edited by anonimnystefy (2011-06-28 02:10:57)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi anonimnystefy,

Do you know Taylor series?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."