Reputation
438
Next privilege 500 Rep.
Access review queues
Badges
4 12
Newest
 Yearling
Impact
~16k people reached

Feb
6
accepted Notational problem
Feb
6
comment Notational problem
Okay. Thanks very much.
Feb
6
comment Notational problem
One more thing... For the last term I have $j$ going from 4 to 3$. Isn't that a problem?
Feb
6
comment Notational problem
so what if I have instead $(c-a_2)(c-a_3)b_1 + (c-a_3)b_2 + b_3$? Would that be $$\sum\limits_{i=1}^3 \left( b_i \prod\limits_{j=i +1}^3 (c-a_j)\right)?$$
Feb
6
comment Notational problem
Thanks JMoravitz. That's exactly what I was after.
Feb
6
comment Notational problem
@JMoravitz Thanks for your helpful comment.
Feb
6
revised Notational problem
added 6 characters in body
Feb
6
comment Notational problem
Can the person who down voted please explain why? Down voting without explaining doesn't help me improving the question if something is wrong it it. thanks.
Feb
6
asked Notational problem
Nov
7
awarded  Yearling
Oct
21
comment Triangle Inequality for norm integral $\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$.
Thanks for not dismissing my comments. I appreciate you taking the trouble to edit the solution. You've been immense! +1
Oct
19
comment Triangle Inequality for norm integral $\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$.
This is what I get. $$\left(\sqrt{\int_a^b(|f|+|f'|)^2dx}+\sqrt{\int_a^b(|g|+|g'|)^2dx}\right)^2 = \\ \int_a^b (|f|+|f'|)^2 dx + 2 \sqrt{\int_a^b (|f|+|f'|)^2 dx \int_a^b(|g|+|g'|)^2 dx} +\int_a^b (|g|+|g'|)^2 dx $$
Oct
19
comment Triangle Inequality for norm integral $\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$.
I understand almost everything. it is the last two lines that are giving me problems. I don't see why\ $$\int_a^b(|f|^2+|f'|^2)dx+2\sqrt{\int_a^b(|f|+|f'|)^2dx\int_a^b(|g|+|g'|)^2dx}+‌​\int_a^b (|g|^2+|g'|^2)dx =\left(\sqrt{\int_a^b(|f|+|f'|)^2dx}+\sqrt{\int_a^b(|g|+|g'|)^2dx}\right)^2 =\left(||f||_1+||g||_1\right)^2 $$
Oct
19
comment Triangle Inequality for norm integral $\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$.
So what is it that am I not getting.
Oct
19
comment Triangle Inequality for norm integral $\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$.
Are there some hidden steps in your solution? I can't justify the going from the second to last line. Expanding the last but one line doesn't give the third line from the bottom. Also I thought $\|f\|_1 = \sqrt {\int_a^b( |f|^2 + |f'|^2)dx} $ but it seems you are saying $\|f\|_1 = \sqrt {\int_a^b (|f|+|f'|)^2 dx}$. Am I missing something?
Oct
18
comment Establishing Triangle Inequality of a particular norm
does this help in finishing the problem?
Oct
18
comment Establishing Triangle Inequality of a particular norm
@LutzL Yes. I know that, but how do I apply that.
Oct
18
revised Establishing Triangle Inequality of a particular norm
added 364 characters in body
Oct
18
asked Establishing Triangle Inequality of a particular norm
Oct
14
revised Property of an integral that vanishes
added 17 characters in body