# Applications of generalized trigonometric functions with two parameters II

@article{Kobayashi2019ApplicationsOG,
title={Applications of generalized trigonometric functions with two parameters II},
author={Hiroyuki Kobayashi and Shingo Takeuchi},
journal={Differential Equations \& Applications},
year={2019}
}
• Published 18 March 2019
• Mathematics
• Differential Equations & Applications
Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the \begin{document}$p$\end{document} -Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of works on GTFs concerning the \begin{document}$p$\end{document} -Laplacian. However, few applications to differential equations unrelated to the $p$-Laplacian are known. We will apply GTFs with two parameters to nonlinear…

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## References

SHOWING 1-10 OF 40 REFERENCES

### Generalized trigonometric functions

is also that of all functions of the form (1 + x2)-2N-c+lQ(x) where Q is a polynomial of degree 4N 2 or lower, the conditions determining the above formula for any a and N are the same as those

### A new form of the generalized complete elliptic integrals

Generalized trigonometric functions are applied to the Legendre-Jacobi standard form of complete elliptic integrals, and a new form of the generalized complete elliptic integrals of the Borweins is

### The basis property of generalized Jacobian elliptic functions

The Jacobian elliptic functions are generalized to functions including the generalized trigonometric functions. The paper deals with the basis property of the sequence of generalized Jacobian

### NIST Handbook of Mathematical Functions

• Mathematics
• 2010
This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.

### Complete p-elliptic integrals and a computation formula of $$\pi _p$$πp for $$p=4$$p=4

The complete p-elliptic integrals are generalizations of the complete elliptic integrals by the generalized trigonometric function $$\sin _p{\theta }$$sinpθ and its half-period $$\pi _p$$πp. It is

### Eigenvalues, Embeddings and Generalised Trigonometric Functions

• Mathematics
• 2011
1 Basic material.- 2 Trigonometric generalisations.- 3 The Laplacian and some natural variants.- 4 Hardy operators.- 5 s-Numbers and generalised trigonometric functions.- 6 Estimates of s-numbers of

### On Generalized Complete (p, q)-Elliptic Integrals

• Mathematics
Acta Mathematica Scientia
• 2021
In this paper, we study the generalized complete ( p, q )-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters, and establish

### Complete $(p,q)$-elliptic integrals with application to a family of means

• Mathematics
• 2015
The complete elliptic integrals are generalized by using the generalized trigonometric functions with two parameters. It is shown that a particular relation holds for the generalized integrals.