This chapter discusses three different ways in which Elliptic functions arise. The periods of a non-constant periodic meromorphic functionare either integral multiples of one period or the sums of integral mult
Elliptic functionModular transformationRamanujanTheta functionVenkatachaliengarThe function $$\\displaylines{\\displaystyle \\Phi(heta;q) = heta + 3\\sum_{k=1}^\\infty\\frac{\\sin(2kheta)q^k}{k(1+q^k+q^{2k})}}$$ occurs in one of Ramanujan's inversion formulas for elliptic integrals...
simulink中用function实现Elliptic滤波器 FIR(Finite Impulse Response)滤波器:有限长单位冲激响应滤波器,又称为非递归型滤波器,是数字信号处理系统中最基本的元件,它可以在保证任意幅频特性的同时具有严格的线性相频特性,同时其单位抽样响应是有限长的,因而滤波器是稳定的系统。因此,FIR滤波器在通信、图像处理、模式识...
Jacobi elliptic function dn, returned as a scalar, vector, matrix, or multidimensional array. More About collapse all The Jacobi elliptic functions are defined in terms of the integral u=∫ϕ0dθ√1−msin2θ. Then sn(u)=sinϕ,cn(u)=cosϕ,dn(u)=√1−msin2ϕ. ...
The Weierstrass elliptic function describes how to get from a torus giving the solutions of an elliptic curve to the algebraic form of the elliptic curve. The differential equation from which Weierstrass elliptic functions arise can be found by expanding about the origin the function . (15) ...
[Sni,Cni,Dni] = ELLIPJ(U,M)returns the values of the Jacobi elliptic functionsSNI,CNIandDNIevaluated for corresponding elements of argumentUand parameterM. The arraysUandMmust be of the same size (or either can be scalar). As currently implemented,Mis real and limited to0 <= M <= 1....
This paper surveys the connection between the elliptic curve E_D: x^3 + y^3 = D and a certain metaplectic form on the cubic cover of GL(3) which has the property that its m,n^{th} Whittaker--Fourier coefficient is essentially the L--series of the curve E_{m^2n}. One may ...
Legendre introduced the symbol Γ for the Gamma function in his (1811–1817, 1, 277). Euler had come across the Gamma function in his (1729). 63. This is Gauss (1812b), which continues (Gauss, 1812a) and is numbered in consecutive sections. 64. The observation that the hypergeometric...
Given the filter order n, the function returns b and a with r samples, where r = n+1 for lowpass and highpass filters and r = 2*n+1 for bandpass and bandstop filters. The transfer function is expressed in terms of b = [b1 b2 ⋯ br] and a = [a1 a2 ⋯ ar] as one of ...
domain in C, and Q: G [1, 1] be a measurable (by Lebesgue) function. We say that a homeomorphism f : G C is a Q-homeomorphism if Mð f ÀÞ Z G QðzÞ Á 2 ðzÞdxdy ð5Þ for every family À of paths in G and for every admissible function 2admÀ...