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ok I am starting to get it,,but what's happens if its a double pole.Do you work out the residues for both functions and multiply the 2 residues together or does it depend eg Gamma[s]Zeta[1-s] so the pole would be at 0. Since the Gamma fn and the Zeta are multiplied together you multiply the...

Hey Is there a method in calculating the residues. Getting the poles is easy but i really don't know how my lecturer gets the residues eg. 1/2(Zeta[s]*Gamma[s/2] where at s = 1 it is Sqrt[Pi]/2 etc how does he do it?

for p = 1 |\frac{1}{2}(a+b)|\leq(\frac{1}{2}|(a+b)|)-ab isnt this false because you subtracting a ab on the RHS?

so you saying that |\frac{1}{2}(a+b)|^{p}\leq(\sqrt[p]{\frac{1}{2}}|(a+b)|)^{p}-pab \leq \frac{1}{2}(|a|^p+|b|^p)

Need help with a complex inequality?? hey! i been trying to do this inequality for a 2 hrs now and can't seem to prove it |\frac{1}{2}(a+b)|^p \leq \frac{1}{2}(|a|^p+|b|^p) where a,b are complex numbers Can anyone suggest a way?? thanks

ok,,thanks i also found the Fundamental Theorem of Algebra which I am reading up now. Thank you everyone! Cheers

I figured that we have to use complex numbers but we weren't told a method how to factorise complex polynomials with say n degree.Can you tell me a method of how to factorize a complex polynomial?? You mentioned that the quote above is the theorema egregium of Algebra which I am having...

the highest we ever gone up to is probably degree 5 that i know of..i'll try look up the theorem and see what you people are talking about

Do you know the name of it because of never heard of it.I wouldn't know where to start.If i have the name i can probably do some research on it and continue from there maybe

I don't see where you going.The roots you can get from the product..do want me to replace z with \cos\theta+i\sin\theta hmmm...with the LHS = (\cos\theta+i\sin\theta)^{n+1}-1=(\cos(n+1)\theta+i\sin(n+1)\theta)-1 and RHS =...

After learning a little latex maybe this looks better z^{n+1} - 1 =\Pi (z - e^\frac{2 \pi i(j+1)}{n+1}) where the product goes from 0<= j <= n

sorry!yes i was missing something in the original equation.So it suppose to look like this (z^(n+1))-1 = Product[(z-exp[2*Pi*i*(j+1)/(n+1)]) , 0<=j<=n] where Product[(z-exp[2*Pi*i*(j+1)/(n+1)]) , 0<=j<=n] = (z-exp[2*Pi*i*(0+1)/(n+1)]*(z-exp[2*Pi*i*(1+1)/(n+1)]*...*(z-exp[2*Pi*i*(n+1)/(n+1)]...

Hey!I have a tut question and I am having problems proving (z^(n+1))-1 = (z-exp[2*Pi*i*(j+1)/(n+1)]) where 0<=j<=n I tried doing it by induction which is easy for the 1st case with n = 1,I assume the case n-1 but then i get stuck with the last case. How will i know that all the z's with...

ok,,so what i have now is correct?Just so i can get started...

btw can you recommend a combinatorics book because he's notes help only a lil plus sometimes he doesn't explain himself properly(by the way we don't have a prescribed textbook) so anything we would be appreciated...

Sorrie haven't replied for a while been kinda busy and sorrie again i thought there was a method because in our notes(which doesn't really help much) he has an example Suppose choose 25 objects from 7 types of objects s.t. every type of object appears at least twice and at most 6 times.. he...

i need help with combinatorics...i need to finda ogf to compute the how many ways can 27 identical walls be distributed into 7 boxes, where the first box can contain at most 9 balls How do this??can you give me a method or explain to me how to do this step by step PLEASE! sAint

helps a bit so i wil just try some more of the exercises and see how it gows thanx..will ask if i need more help Saint

I still don't get how you do that... eg summation from k=0 to n (n k) {k is underneath n so basically its choosing k from n} = 2^n

How do you do a combinatorial proof? hey ppl! Im having a hard time trying to do a combinatorial proof! How do you start? WHat do you look at?? A general method would really help! Thanx SAint_n

1) i don't know how to use MATLAB / mathematica (if u were thinking about it) 2) Gotta show all the working out hahaha

i was thinking of approximating \int\frac{sinx}{x}dx\ by changing it into an alternating series where T(n) = \mid\int\frac{sinx}{x}dx\mid where n = 1... infinity and waz even thinking of using complex analysis to integrate it and we see when i get through it but I am also trying to...

sorry! i forgot to mention it. But looks like everyone got the idea that it was (0,infinity) which it what i wanted. Found out that the method i mentioned before... i did a stupid thing by turning the minus to plus, DOPE!thanx

writing T(n) = \mid\int\frac{sinx}{x}dx\mid Can u write sinx as a power series then dividing by x and integrating it then you get T(n) so T(n) = x + (x^3)/(3!3) + (x^5)/(5!5) + ... since i made my interval ( (n-1)\pi , n\pi) Why am i getting t(n) > t(n-1) What am i doing wrong??Can it...

thanx for the help!My light bulb just went on!Couldnt av done it without ya Saint_n

thanx for the help ppl!My light bulb just went on!Couldnt av done it without yas Saint_n

integral of sinx/x exists? #1 saint_n Registered User Join Date: Apr 2004 Posts: 3 integrating sinx/x between (0,infinty)? -------------------------------------------------------------------------------- hey ppl! Can you help me by giving me a method or how you would go...

integrating sinx/x between (0,infinty)? hey ppl! Can you help me by giving me a method or how you would go around to prove that this \mid\int\frac{sinx}{x}dx\mid exists. Thanx Saint_n

How will you do \int\frac{sinx}{x}dx from zero to infinity. Which can be written as a alternating series T subscript n =\mid\int\frac{sinx}{x}dx\mid over intervals ((n-1)\pi,n\pi) but how do show as n tends to infinity that T(n) tends to 0? cos i can't integrate it

limits..proving they exist? Wot do u have to do to prove that an intergral exists.?? I know how to do it if the integrals bounds are given ( example, [a,b]) but wot if the integral is from x till infinity??