query: Second-order term of Baker-Campbell-Hausdorff formula
positive_passages.docid: 143765
positive_passages.text: To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
negative_passages.docid: 150626
negative_passages.text: General formula or a pattern for the $n$th derivatives of $e^{f(x)}$?
negative_passages.docid: 100007
negative_passages.text: Express partial derivatives of second order (and the Laplacian) in polar coordinates
negative_passages.docid: 35298
negative_passages.text: A question about the higher-order Weyl variation for the geodesic distance
negative_passages.docid: 49073
negative_passages.text: how to obtain solution for $u_t+u=u_{xx}$
negative_passages.docid: 116520
negative_passages.text: formula for the $n$th derivative of $e^{-1/x^2}$
negative_passages.docid: 3201
negative_passages.text: Landau & Lifshitz's Approach (contour method) on the WKB connection formulas
negative_passages.docid: 119552
negative_passages.text: Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$
negative_passages.docid: 8844
negative_passages.text: Higher-order partial derivatives w.r.t. variable raised to some power
negative_passages.docid: 105293
negative_passages.text: Proof of the second symmetric derivative
negative_passages.docid: 36990
negative_passages.text: Notation of the second derivative - Where does the d go?
negative_passages.docid: 80164
negative_passages.text: Taylor expansion of a function containing QPochhammer[q, q, n]
negative_passages.docid: 71708
negative_passages.text: Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
negative_passages.docid: 129765
negative_passages.text: Mean value theorem for the second derivative, when the first derivative is zero at endpoints
negative_passages.docid: 23093
negative_passages.text: Proof of recursion formula for Stirling number of the second kind
negative_passages.docid: 37192
negative_passages.text: proof of the second generalized mean value theorem for integrals
negative_passages.docid: 26113
negative_passages.text: Proving the functional equation $\theta (x) = x^{-\frac{1}{2}} \theta (x^{-1})$ from the Poisson summation formula