| viXra.org > Functions and Analysis > 2010 |
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| viXra.org > Functions and Analysis > 2010 |
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[4] viXra:2010.0245 [pdf] submitted on 2020-10-30 08:48:22
Authors: Claude Michael Cassano
Comments: 6 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
A formula for all the Half-Integer Bessel ODE is produced using my article "Exact solution of ODEs Vector Space Transformation Technique, Part 2".
(In an earlier publication I produced an algorithm for the Bessel hallf-integer solutions, but advancements on the Vector Space Transformation Technique allowed an actual formula to be produced (as well as further results)
Category: Functions and Analysis
[3] viXra:2010.0211 [pdf] submitted on 2020-10-26 20:23:53
Authors: Claude Michael Cassano
Comments: 7 Pages. [Corrections made to conform with the requirements on the Submission Form]
Since the number of linearly independent solutions of an HLODE equals the order of the HLODE, the dimension of the solution set of an HLODE is it's order; so the dimension of all HLODEs of the same order is this order. Thus, a first order HLODE may be solved exactly using the single HLODE ; but higher order non-elementary HLODEs require that order number of equations to solve such HLODEs - i.e. usage of linear transformations between linearly independent HLODE solution sets of that same order. The first order HLODE being of dimension 1 may be solved exactly by itself. Higher order HLODEs are subject to condition that the additional dimensional HLODEs must also be satisfied.
Category: Functions and Analysis
[2] viXra:2010.0210 [pdf] replaced on 2023-08-11 10:25:47
Authors: Michael Parfenov
Comments: 16 Pages.
To automate cumbersome, error-prone and tedious manual procedures of calculations with quaternionic holomorphic (ℍ -holomorphic) functions we have developed and present here a special programmes pack in the Wolfram Mathematica® programming language. By using this pack a lot of examples of ℍ -holomorphic functions is processed. They give conclusive evidence that the so-called essentially adequate theory of quaternionic holomorphy is true. All considered ℍ -holomorphic functions are built from complex holomorphic ones in accordance with the general constructing rule defined earlier. At that combinations of ℍ -holomorphic functions are built from the simplest basis (irreducible) ℍ -holomorphic functions by using the usual rules of quaternionic algebraic operations.
Category: Functions and Analysis
[1] viXra:2010.0050 [pdf] submitted on 2020-10-07 19:13:47
Authors: Saburou Saitoh
Comments: 13 Pages.
In this paper, we will discuss the Laplace transform from the viewpoint of the division by zero calculus with typical examples. The images of the Laplace transform are analytic functions on some half complex plane and meanwhile, the division by zero calculus gives some values for isolated singular points of analytic functions. Then, how will be the Laplace transform at the isolated singular points? For this basic question, we will be able to obtain a new concept for the Laplace integral.
Category: Functions and Analysis
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