query: Definite integrals and infinite sums with known (conjectured) closed forms but no proof
positive_passages.docid: 28109
positive_passages.text: Conjectural closed-form representations of sums, products or integrals
negative_passages.docid: 98941
negative_passages.text: Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
negative_passages.docid: 39659
negative_passages.text: Is there a closed formula for this summation?
negative_passages.docid: 8705
negative_passages.text: Evaluation of $\sum_{x=0}^\infty e^{-x^2}$
negative_passages.docid: 74454
negative_passages.text: Sophomore's dream: $\int_0^{1} x^{-x} \; dx = \sum_{n=1}^\infty n^{-n}$
negative_passages.docid: 101908
negative_passages.text: Solving summations of form $\sum_{i=0}^{\infty} i^kx^i$ without Differentiation and Integration
negative_passages.docid: 119606
negative_passages.text: Closed form of summation
negative_passages.docid: 131739
negative_passages.text: Is my proof of the additivity property of Riemann integral correct?
negative_passages.docid: 17214
negative_passages.text: Transfinite series: Uncountable sums
negative_passages.docid: 128572
negative_passages.text: How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
negative_passages.docid: 57759
negative_passages.text: Determining the infinite sum $\sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1}$
negative_passages.docid: 52774
negative_passages.text: Computing an infinite sum using the Residue theorem
negative_passages.docid: 19914
negative_passages.text: Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
negative_passages.docid: 121617
negative_passages.text: Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$
negative_passages.docid: 157972
negative_passages.text: Find a closed form expression for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
negative_passages.docid: 145183
negative_passages.text: finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
negative_passages.docid: 78116
negative_passages.text: What is the most elementary proof that $\lim_{n \to \infty} (1+1/n)^n$ exists?