20040821, 15:14  #1 
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Polynomial sequence
What is the next polynomial in this sequence?
1. xy 2. x^{3} + xy^{2} 3. 5x^{3}y + xy^{3} 4. 5x^{5} + 18x^{3}y^{2}+xy^{4} 5. ?? 
20041014, 12:19  #2  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Polynomial sequence
Quote:
So whats the answer Travis? Please give us the method or line of reasoning Mally 

20041014, 15:55  #3 
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
0. f(x) = sec x
1. f'(x) = sec x tan x 2. f''(x) = sec x tan^{2} x + sec^{3} x . . . replace sec x with x and tan x with y to get: 1. xy 2. xy^{2} + x^{3} etc. I don't have the answer on me right now, but I can dig it up 
20041015, 00:21  #4 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Using Mathematica, the next polynomial is:
61(x^5)y + 58(x^3)(y^3) + x(y^5) 
20041015, 15:18  #5  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Polynomial sequence
Quote:
Thank you Travis. Very ingenious of you. Its not how far one can go but the method that counts. Thats one more problem to add to my notes. Thats one more type I can put under my hat. :surprised Mally 

20041015, 15:47  #6  
Bronze Medalist
Jan 2004
Mumbai,India
4004_{8} Posts 
Polynomial Sequence
Quote:
I am afraid you have jumped a couple of steps ahead and a couple is putting it mildly. On inspection I found your coefficients to be too high I have had a bad experience with Mathematica and am not surprised at your result. To quote Travis' original problem which I noted he has given the third term as 5(x^3)y +x(y^3) The 4th term he has given is 5(x^5) +18 (x^3)(y^2) +x(y^4). You can take it from there Jinydu. Altho' 5 is a prime I doubt if a prime as high as 61 should figure so soon if ever! But I leave it to the experts on the subject to thrash this out. I for one am satisfied in not going any further unless it is of practicaL value in some field or the other. Thanks all the same. Its the good intention and not the result that matters to me. Mally 

20041015, 16:05  #7 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Polynomial Sequence
Jinydu.
I have just read the original post of Travis which I couldnt locate and referred to my notes instead! He has asked for the 5th in sequence and maybe you may be right after all. I am very sorry if that is the case and your labour and interest has not gone in Vain. Mally 
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