List questions from closed-form

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Is there a closed-form for $\sum_{k=0}^{\infty} \frac{1}{(k!)^2}$?

Published on 06 Apr 2026 - 1:24

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Please help solve the following recurrences

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Proving a Problem has a Closed Form Solution

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How to find $\int_0^\pi (\log(1 - 2a \cos(x) + a^2))^2 \mathrm{d}x, \quad a>1$?

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How to derive a closed form of a simple recursion?

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What is the formula of: $a^{0} + a^{1} + a^{2} + ... + a^{n-1} + a^{n}$?

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Recurrence equation question

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Stuck on solving recurrence relation

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Double sum with binomial coefficients $\sum_{1\le i<j\le m} \sum_{\substack{1\le k,l\le n \\ k+l\le n}}{n\choose k} {n-k\choose l} (j-i-1)^{n-k-l}$

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Finding the expression for $q_n$

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Infinite Product $\prod_{n=1}^\infty\left(1+\frac1{\pi^2n^2}\right)$

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Finding a Linear Recurrence Relation

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266

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Calculate or approximate $\sum\limits_{k=801}^{849}{ \binom {2400} {k}} $

Published on 15 Apr 2013 - 19:02

916

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Tough Inverse Fourier Transform

Published on 26 Apr 2013 - 15:14

List Question

Find the closed form for $\int_{0}^{1}\left(x^k+{\ln{x}\over 1-x}\right)^2dx=f(k)$

Is there a closed-form for $\sum_{k=0}^{\infty} \frac{1}{(k!)^2}$?

Please help solve the following recurrences

Proving a Problem has a Closed Form Solution

How to find $\int_0^\pi (\log(1 - 2a \cos(x) + a^2))^2 \mathrm{d}x, \quad a>1$?

How to derive a closed form of a simple recursion?

What is the formula of: $a^{0} + a^{1} + a^{2} + ... + a^{n-1} + a^{n}$?

Recurrence equation question

Stuck on solving recurrence relation

Double sum with binomial coefficients $\sum_{1\le i<j\le m} \sum_{\substack{1\le k,l\le n \\ k+l\le n}}{n\choose k} {n-k\choose l} (j-i-1)^{n-k-l}$

Finding the expression for $q_n$

Infinite Product $\prod_{n=1}^\infty\left(1+\frac1{\pi^2n^2}\right)$

Finding a Linear Recurrence Relation

Calculate or approximate $\sum\limits_{k=801}^{849}{ \binom {2400} {k}} $

Tough Inverse Fourier Transform

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