query: Limit of the reciprocal of the mean harmonic
positive_passages.docid: 145614
positive_passages.text: Proving one limit is equal to another
negative_passages.docid: 103285
negative_passages.text: Limit of a periodic function
negative_passages.docid: 109103
negative_passages.text: Proof that $\lim_{m\to\infty}(1+\frac{r}{m})^{mt}=e^{rt}$
negative_passages.docid: 88790
negative_passages.text: Positive harmonic function on $\mathbb{R}^n$ is a constant?
negative_passages.docid: 120533
negative_passages.text: A harmonic function with sublinear growth at infinity is constant
negative_passages.docid: 77645
negative_passages.text: Generalized mean value theorem
negative_passages.docid: 99149
negative_passages.text: Limit of the difference between two exponential functions
negative_passages.docid: 22598
negative_passages.text: When does the limit $\lim_{(x,y)\to(0,0)} \frac{x^ky^l}{x^{2p}+y^{2q}}$ exist?
negative_passages.docid: 124061
negative_passages.text: Prove the reciprocal of a function is integrable if it is bounded
negative_passages.docid: 67485
negative_passages.text: The ratio $\frac{u(z_2)}{u(z_1)}$ for positive harmonic functions is uniformly bounded on compact sets
negative_passages.docid: 111255
negative_passages.text: Gauss's mean value theorem problem
negative_passages.docid: 70621
negative_passages.text: Question concerning the mean-value property
negative_passages.docid: 39674
negative_passages.text: Rolle's Theorem and the Mean Value Theorem
negative_passages.docid: 42302
negative_passages.text: Use of Holder inequality in gradient estimate for harmonic function.
negative_passages.docid: 113141
negative_passages.text: Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
negative_passages.docid: 49511
negative_passages.text: Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?
negative_passages.docid: 32955
negative_passages.text: Value of $\lim_{n\to\infty}\sum_{j=0}^{[\frac{n}{2}]}\frac{1}{n}f(\frac{j}{n})$