Trying this, it seems like the taylor expansion doesn't aid the convergence because the terms of the resultant series are either unchanged sine series (when they are even), or are slightly increased in amplitude when the exponential term is a product of two of 3 ,5 ,7 , 9, etc
For example
f(x)...
Yes, your wording for uniform convergence is similar to the one in my book, with the minor exception that it is for any epsilon>0, there exists an N such that for all n>N etc
I'm having some difficulty understanding how the convergence properties aren't based on x.
If I take |f_n(x)-f(x)| <...
It's also important to note that the Fed's QE program was literally meant to push people from keeping their money in low yield savings accounts into equities which is what has driven up American stock prices in general over the past few years. Nothing particular about the DJIA itself led to...
Hello everyone,
I'm currently an investment banker but in undergrad I was really interested in mathematics.
I took most of my school's real analysis, complex analysis, algebra and number theory courses, but alas the lure of financial stability pulled me away from graduate school in mathematics...
Homework Statement
I came across a problem where f: (-π/2, π/2)→ℝ where f(x) = \sum\limits_{n=1}^\infty\frac{(sin(x))^n}{\sqrt(n)}
The problem had three parts.
The first was to prove the series was convergent ∀ x ∈ (-π/2, π/2)
The second was to prove that the function f(x) was continuous...