A Cosine Integral: Recurrence, Wallis, and Euler
Three evaluations of a cosine integral, using integration by parts, angle addition and Wallis integrals, or Euler's formula.
Random thoughts
Also see the structured notes in my bookshelf.
Evaluating a Sine Integral with Two, One, or No Parameter Derivatives
Three evaluations of a sine integral, using two parameter derivatives and an ODE, one derivative and residues, or a direct contour integral.
Solving Fresnel Integrals by Schwinger Parameterization and Complex Analysis
A detailed evaluation of the Fresnel integrals using a regulated Schwinger parameter and a contour rotation in the complex plane.
A Feynman-Parameter and Residue-Theorem Evaluation of an Arctangent Integral
A detailed evaluation of an improper integral using differentiation under the integral sign, residues, and a symmetric double integral.
Building $\mathbf{k}_{\parallel}$ Wavelet Pulses in MaxwellLink
A technical note on how MaxwellLink's k_parallel_pulse builds real-space molecular drives and mode-space photonic drives in the multimode Fabry-Perot cavity solver.
Computing Large Scale Matrices Product with Generalized Inverse \(FSF^+\)
A numerical linear algebra note on generalized inverses, SVD, scipy.linalg.solve, Cholesky decomposition, and LU decomposition for \(FSF^+\).
Complex-Shifted Gaussian Integral and the Heat Kernel
A contour proof that a complex-shifted Gaussian integral equals the ordinary one, with an application to the free-particle heat kernel.
A Residue-Theorem Evaluation of \(\int_0^1 \frac{\ln x}{x^2-x-1}\,\mathrm{d}x\)
A residue theorem evaluation of a superhard real integral.
No posts match your search and topic.