Solving the Basel problem using Gauss's law - Physics Forums
2018年6月20日 · Imagine a lighthouse that has absolute brightness 1. The apparent brightness then follows an inverse-square law. Now imagine an infinite number line with positive integers only (and 0), with a lighthouse at each integer. The Basel problem then becomes: find the apparent brightness at the 0 point. This is simple enough.
Basel problem, primes and π²/6 - Physics Forums
2015年12月15日 · Basel problem, primes and π²/6 I; Thread starter Borek; Start date Dec 15, 2015; Tags Primes Dec 15 ...
Basel Problem Integral: Solving with Calculus - Physics Forums
2021年1月12日 · Summary:: Using an integral and taylor series to prove the Basel Problem The Basel problem is a famous math problem. It asked, 'What is the sum of 1/n^2 from n=1 to infinity?'. The solution is pi^2/6. Most proofs are somewhat convoluted. I'm attempting to …
The Basel Problem: A Solid Solution Using Derivatives and Integrals
2010年6月3日 · The Basel problem has been a topic of interest for centuries and it is exciting to see new solutions being proposed. The use of derivatives and integrals in this solution is a clever approach and shows the power of mathematical tools in solving complex problems.
Euler's solution to the Basel problem - Physics Forums
2010年5月6日 · Euler Solution to the Basel Problem. Oct 26, 2013; Replies 1 Views 2K.
Why Parseval's Identity Fails for Higher Exponents in Basel Problem
2012年8月13日 · Unlike for the Basal problem, the Fourier coefficient [itex]a_0[/itex] for the problem you are doing is not zero. When you account for the [itex]a_0^2[/itex] term, you should get the correct result. (By the way, Euler solved the problem using different methods than Parseval's theorem).
How can we prove that the sum of alternating squares equals pi …
2012年9月7日 · The Basel Problem is a well known result in analysis which basically states: \\frac{1}{1^2} + \\frac{1}{2^2} + \\frac{1}{3^2} + \\frac{1}{4^2} + ... = \\frac{\\pi^2}{6} There are various well-known ways to prove this. I was wondering if there is a similar, simple way to calculate the value of the...
Can Euler's Method Solve Higher Order Sums in the Basel Problem?
2013年2月26日 · Is it possible to extend Euler's method of solving the Basel Problem to higher orders of even n (expanding the sine series, collecting the roots, and equating terms)? Physics news on Phys.org Unexpected shape of lead-208 nucleus prompts reevaluation of …
Converging to the Basel Problem: Solving for Poles on the Real Axis
2013年6月16日 · I Solving the Basel problem using Gauss's law. Jun 21, 2018; Replies 4 Views 2K.
Euler Solution to the Basel Problem - Physics Forums
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