Functions and Analysis

2403 Submissions

[6] viXra:2403.0111 [pdf] submitted on 2024-03-22 07:37:28

Advanced Continued Fraction Approximations and Bounds for the Gamma Function and the Generalized Wallis

Authors: YunJong Kang, HyonChol Kim HyonChol Kang, Kwang Ri
Comments: 26 Pages.

In this paper, we provide a main method for construction of continued fraction based on a given power series using Euler connection. Then we establish very innovative results in continued fraction approximation for the Gamma function as applications of our method. Also new continued fraction bounds for the Gamma function are obtained. Finally new continued fraction approximations and bounds for Wallis ratio are established.
Category: Functions and Analysis

[5] viXra:2403.0093 [pdf] submitted on 2024-03-19 19:48:12

Continued Fraction Approximation and Bounds for the Psi Function

Authors: Pak SongBom, Han CholSok, Kim HyonChol
Comments: 11 Pages.

In this paper, we provide a new continued fraction approximation for the psi function. Then we establish continued fraction bounds for the psi function.
Category: Functions and Analysis

[4] viXra:2403.0088 [pdf] submitted on 2024-03-18 07:43:46

Unification of the Hiperoperators Theory and the Serial Operators Theory

Authors: Juan Elias Millas Vera
Comments: 4 Pages.

In this paper I combined all the hiperoperations theory with the theory of series of functions developing new notation when it was necessary.
Category: Functions and Analysis

[3] viXra:2403.0086 [pdf] submitted on 2024-03-19 02:52:53

Zernike Expansion of Chebyshev Polynomials of the First Kind

Authors: Richard J. Mathar
Comments: 8 Pages.

The even Chebyshev Polynomials T_i(x) can be expanded into sums of even Zernike Polynomials R_n^0(x), and the odd Chebyshev Polynomials can be expanded into sums of odd Zernike Polynomials R_n^1(x). This manuscripts provides closed forms for the rational expansion coefficients as products of Gamma-functions of integer and half-integer arguments.
Category: Functions and Analysis

[2] viXra:2403.0068 [pdf] replaced on 2024-10-18 12:23:43

A Proof of the Kakeya Maximal Function Conjecture Via Big Bush Argument

Authors: Johan Aspegren
Comments: 7 Pages.

In this paper we reduce the Kakeya maximal function conjecture to the tube sets of unit measure. We show that the Kakeya maximal function is essentially monotonic. So by adding tubes we can reduce the conjecture to the case of unit measure tube set if we allow the technicality that there are possibly two tubes on the same direction. Then we proof the Kakeya maximal function conjecture from our lemma.
Category: Functions and Analysis

[1] viXra:2403.0054 [pdf] replaced on 2024-03-13 22:26:33

A New Numerical Interpretation of the Concept of Exponentory (Θ Notation)

Authors: Juan Elias Millas Vera
Comments: 3 Pages.

In this paper I show a possible change in the theory of series beyond product. Instead of a resolution Bottom-to-Top we will see a necessary application of the method for exponents that is a process Top-to-Bottom. That implies a change in the numerical results in a same proposition of a series.
Category: Functions and Analysis