Basel problem
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Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed...
Basel
'Basel Problem' was solved in the city, which is regarded as one of the most important achievements in mathematics. The official language of Basel is...
Pi
simple solution for this infinite series was a famous problem in mathematics called the Basel problem. Leonhard Euler solved it in 1735 when he showed it...
Euler–Maclaurin formula
}}+\int _{m}^{n}f^{(7)}(x){\frac {P_{7}(x)}{7!}}\,dx.\end{aligned}}} The Basel problem is to determine the sum 1 + 1 4 + 1 9 + 1 16 + 1 25 + ⋯ = ∑ n = 1 ∞...
−2
positive; the inverse-square law; grid turbulence decay; and the Basel problem. The Basel problem states that the sum of the square reciprocals of natural numbers...
Riemann zeta function
computed by Euler. The first of them, ζ(2), provides a solution to the Basel problem. In 1979, Roger Apéry proved the irrationality of ζ(3), and got the...
Prime number
Leonhard Euler and his first major result, the solution to the Basel problem. The problem asked for the value of the infinite sum 1 + 1 4 + 1 9 + 1 16 +...
Leonhard Euler
accomplishments, solving several unsolved problems in number theory and analysis, including the famous Basel problem. Euler has also been credited for discovering...
List of sums of reciprocals
"Euler's number"). The sum of the reciprocals of the square numbers (the Basel problem) is the transcendental number π2 /6 , or ζ(2) where ζ is the Riemann...
Coupon collector's problem
{1}{1^{2}}}+{\frac {1}{2^{2}}}+\cdots +{\frac {1}{n^{2}}}+\cdots } (see Basel problem). Bound the desired probability using the Chebyshev inequality: P ...