I demonstrate that [2.e^(-π.x)+1] is a close approximation to several complicated formulas.
For everybody , with minimal knowledge of complex analysis to understand the marvelous Zeta function and the RH. And to comprehend also the basic property of the Theta function.
Inhaltsverzeichnis (Table of Contents)
- From Suspicion to Something Spectacular
- Dirac's Principle
- Fourier's Expansion of the function f(x) = e-a.x
- Fourier's Expansion of the function g(x) = e- [π /a].x
- Fourier's Integral
- Very Close Approximations
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This text aims to explore the relationship between mathematical concepts, particularly Fourier analysis, Dirac's delta function, and the Gamma function. It delves into the author's discoveries and insights concerning these concepts, highlighting their connections and implications.
- Fourier analysis
- Dirac's delta function
- Gamma function
- Mathematical discovery and insight
- Approximations and their significance
Zusammenfassung der Kapitel (Chapter Summaries)
- From Suspicion to Something Spectacular: This section introduces the author's initial suspicion and subsequent discovery of a remarkable relationship between mathematical concepts. It highlights the role of Fourier analysis and the concept of Dirac's delta function in this discovery.
- Dirac's Principle: This chapter delves deeper into the significance of Dirac's principle in relation to Fourier series, integrals, and Taylor series. It highlights the author's contribution to a deeper understanding of this principle.
- Fourier's Expansion of the function f(x) = e-a.x: This chapter presents a detailed mathematical exploration of the Fourier expansion of the function f(x) = e-a.x. It demonstrates the application of the concepts previously discussed and showcases the author's methodology.
- Fourier's Expansion of the function g(x) = e- [π /a].x: This section follows a similar structure to the previous chapter, applying the same principles to the Fourier expansion of the function g(x) = e- [π /a].x.
- Fourier's Integral: This chapter discusses the Fourier integral, emphasizing its connection to the previous expansions and providing further insights into the author's work.
- Very Close Approximations: This section concludes the text with a presentation of various approximations, highlighting their remarkable accuracy and demonstrating the practical applications of the concepts explored throughout the work.
Schlüsselwörter (Keywords)
The central focus of this text lies in the interconnectedness of mathematical concepts, particularly Fourier analysis, Dirac's delta function, Gamma function, mathematical discovery, and approximations. The author's unique perspective and contributions in these areas are highlighted, showcasing the significance of these concepts in mathematical understanding.
- Quote paper
- Prof. Dr. med. John Bredakis (Author), 2013, From suspicion to something spectacular: My Fourier's analysis, Munich, GRIN Verlag, https://www.grin.com/document/265471
