Alois Schiessl

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20242026

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math.GM2026

A fixed point iteration method for the arctangent with any odd order of convergence based on sine and cosine

Alois Schiessl

In this paper, we present a fixed point method for the arctangent based on sine and cosine. Let $t \in R^{+}$ and $P \in N$ . We define: \[T\left(x\right)=x-\sum_{k=…

math.GM2026

A fixed-point iteration method for the number Pi with arbitrary odd order of convergence based on the sine function

Alois Schiessl

In this paper, we present a fixed point method for high-precision computation of number $π$ based on the sine function. Let $P \in N$ . We define the function: \[ S\left(x\r…

math.GM2026

A root finding method with arbitrary order of convergence

Alois Schiessl

Let $a \in R^{+} \ {0}$ and $M \in N$ . We consider the equation $t^{M} - a = 0$ , which is equivalent to $1 - \frac{t ^{M}}{a} = 0 .$ The real solution is $\s…

math.GM2025

Just another method for generating series of even powers of number Pi

Alois Schiessl

In our previous publication we have shown a method for calculating series of even powers of $π$ based on the product representation of the $s in c$ function. We refer the readers to…

math.GM2024

Series for even powers of Pi by generalization Euler's method for solving the Basel Problem

Alois Schiessl

The purpose of this paper is to present series expansions for even powers of the number $π$ . This is accomplished by generalizing Euler's method for solving the Basel Problem, whic…