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An Electrical Method for Compounding Sine Functions
Review of Scientific Instruments, 1940An electrical device is described for evaluating the series ΣAi sin aix. For each term in the series there is constructed one compounding element composed of three coils; a long solenoid acting as a primary (60-cycle a.c.) within which are mounted two short secondary coils, one a rotor (order of 1/5 r.p.m.) and the other a stator. The mutual inductance
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Van Vleck’s functional equation for the sine
Aequationes mathematicae, 2015Let \(S\) be a semigroup, \(\tau:S\to S\) an involution of \(S\) and \(z_0\in S\) be a fixed element of the center of \(S\). The author determines the solution \(f:S\to\mathbb{C}\) of the functional equation \[ f(x\tau(y)z_0)-f(xyz_0)=2f(x)f(y)\quad(x,y\in S), \tag{1} \] which is a natural generalization of \textit{E. B.
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Shintani’s prehomogeneous zeta functions and multiple sine functions
Rendiconti del Circolo Matematico di Palermo, 2005For \(n\geq 1\) let \(Z_n(s)\) be Shintani's prehomogeneous zeta function associated to the space of symmetric matrices. The author proves that for \(n\equiv 1\pmod 4\), \(n\neq 1\), the function \( Z_n(s)\) has a simple zero at \(s=0\), and \[ Z_n'(0)=-(-4)^{\frac{1-n}{4}}(\zeta(-1)\zeta(-3)\dots \zeta(-(n-2)))^2\log\left(\prod_{k=1}^{\frac{n-1}{4}}S_{
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A Generalization of the Sine Function
The American Mathematical Monthly, 1957openaire +1 more source
The Remarkable Sine Functions.
The American Mathematical Monthly, 1969P. E. Bedient, A. I. Markushevich
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Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function
Electronics, 2020Xiaoyi Feng, Pengfei Ding, Lin Fa
exaly
A new class of probability distributions via cosine and sine functions with applications
Communications in Statistics Part B: Simulation and Computation, 2019Christophe Chesneau, Hassan S Bakouch
exaly