Functions and Analysis

2002 Submissions

[3] viXra:2002.0508 [pdf] replaced on 2020-10-04 09:51:59

On Certain Finite Sums of Inverse Tangents

Authors: Martin Nicholson
Comments: 10 Pages. A new theorem is added.

An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are discussed.
Category: Functions and Analysis

[2] viXra:2002.0366 [pdf] submitted on 2020-02-19 16:03:00

Division by Zero Calculus For Differentiable Functions in Multiply Dimensions

Authors: Saburou Saitoh
Comments: 14 Pages. I am writing a book on the division by zero and so I am asking for kind suggestions and comments on the topics.

Based on the preprint survey paper, we will give a fundamental relation among the basic concepts of division by zero calculus and derivatives as a direct extension of the preprints which gave the generalization of the division by zero calculus to differentiable functions. Here, we will consider the case of multiply dimensions. In particular, we will find a new viewpoint and applications to the gradient and nabla.
Category: Functions and Analysis

[1] viXra:2002.0060 [pdf] replaced on 2020-02-18 07:50:48

A Short Remark on the Result of Jozsef Sandor

Authors: Yogesh J. Bagul
Comments: 3 Pages.

We point out that Corollary 2.2 in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by Jozsef Sandor is slightly incorrect since its proof contains a gap. Fortunately, the proof can be corrected and this is the main aim of this note.
Category: Functions and Analysis