# Questions tagged [sequences-and-series]

for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.

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### For which values of $ x$ we have $\sum\limits_{n=0}^{\infty}x^{\tan(n!)-n!}$ converges?

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### Does this formula correspond to a series representation of the Dirac delta function $\delta(x)$?

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### (Dis)continuity of periodic functions with non-summable Fourier series

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### Square root of a sequence given by a linear recurrence relation

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### Classification of the behaviours of the logistic map

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### A binomial coefficient identity involving two parameters

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### Is there a known condition for partial sums of a decreasing positive sequence to take all values up to the total sum?

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### Are there any extensive treatments on rational zeta series?

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### On Köthe sequence spaces

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### What is the collection of series that amount to $\gamma$ deduced by Ramanujan?

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### Convergence of a nonlinear iterative sequence

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### Kolmogorov tightness criterion for stochastic processes

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### Spherical harmonics expansion

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### Is asymptotic growth bound on a sequence equivalent to an asymptotic growth bound on its partial sum?

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### Analyze a complicated double summation

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### Less fundamental applications of Zeta regularization:

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### Does this series, related to the Hasse/Ser series for $\zeta(s)$, converge for all $s \in \mathbb{C}$?

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### Series and sequences in physical systems & closed form expressions

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### Monotonic and bounded sequences throughout mathematics [closed]

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### Maximizing the length of a sequence under constraints

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### Do infinitely nested radicals have any applications?

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### Prove the supremum of Mittag-Leffer function

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### For $x$ irrational, is $a_{n} =\sum_{k=1}^{n}(-1)^{⌊kx⌋}$ unbounded?

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### Subdividing a sequence such that sum is somewhat equally distributed

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### What are some interesting relationships between pi and phi? [closed]

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### An inequality involving square roots and sums

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### Efficient computation of $\sum_{i=1}^{\sqrt{n}} i^2\cdot\left\lfloor{\frac n{i^2}}\right\rfloor$

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### Sequence estimate for slow variation to study the wandering rate of a set

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### Ranking graph's nodes by score propagation

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### Series representation for $\log(|\zeta(\frac{1}{2}+it)|)$

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### Sequence $(a_n)$ for which $ \prod_{n=1}^{\infty} \left ( 1- \dfrac{m}{a_n +m} \right ) =r.$ [closed]

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### Non-uniqueness of (Galerkin) approximations and convergent subsequences without the axiom of choice?

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### Proof of a discrete isoperimetric inequality

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### Sequence of least prime-multiples with smallest Hamming weight

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### Mean and logarithmic values for arithmetic function

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### Comparison of product topology and colimit topology in sequence spaces

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### Sum of $\sum_{1\leq k\leq k'\leq n}\frac{k^{\alpha}}{k'^{\alpha}}$ [closed]

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### Logconcavity of height of Dyck paths

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### O(1) or o(logn) discrepancy for multiples of an irrational for at least one sub interval

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### Properties of sequences associated to Nakayama algebras

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### About the distribution of Fibonacci numbers that are primes

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### How to prove the relationship between Stern's diatomic series and Lucas sequence $U_n(x,1)$ over the field GF(2)?

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### About the sum $S(p_n)=\sum_{1\le k\lt n}\,p_n\mod\;p_k$

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### Is there a rectangular tiling based on the Padovan sequence? [closed]

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### Boundedness of $\chi_{\{f_n=0\}}$ in the BV norm

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### Find the closed-form expression for $c_n$ of this recursive sequence [closed]

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### On the series of the product of the terms of two sequences whose respective series are one convergent and the other not [closed]

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### Positions in the Wythoff array

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### Is it possible to determine whether the sequence $\,a_0=p,\;a_{n+1}=(a_n-2)\cdot a_n+2\,$ will reach another prime number?

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