Khare, Avinash ; Sukhatme, Uday (2002) Cyclic identities involving Jacobi elliptic functions Journal of Mathematical Physics, 43 (7). pp. 3798-3806. ISSN 0022-2488
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Official URL: http://jmp.aip.org/resource/1/jmapaq/v43/i7/p3798_...
Related URL: http://dx.doi.org/10.1063/1.1484541
Abstract
We state and discuss numerous new mathematical identities involving Jacobi elliptic functions sn(x,m), cn(x,m), and dn(x,m), where m is the elliptic modulus parameter. In all identities, the arguments of the Jacobi functions are separated by either 2K(m)/p or 4K(m)/p, where p is an integer and K(m) is the complete elliptic integral of the first kind. Each p-point identity of rank r involves a cyclic homogeneous polynomial of degree r (in Jacobi elliptic functions with p equally spaced arguments) related to other cyclic homogeneous polynomials of degree r-2 or smaller. We algebraically demonstrate the derivation of several of our identities for specific small values of p and r by using standard properties of Jacobi elliptic functions. Identities corresponding to higher values of p and r are verified numerically using advanced mathematical software packages.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Physics. |
Keywords: | Jacobi Elliptic Functions; Cyclic Identities |
ID Code: | 83271 |
Deposited On: | 20 Feb 2012 09:26 |
Last Modified: | 19 May 2016 00:11 |
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