Analysis of the Construction Thought of Generating Functions

DOI: https://doi.org/10.62517/jnse.202517201

Author(s)

Lewei Huang1,*, Xuran Li1, Mingyue Cao2

Affiliation(s)

1Department of Mathematics, Huzhou University, Huzhou, Zhejiang, China 2Department of Physics, Huzhou University, Huzhou, Zhejiang, China *Corresponding Author

Abstract

In this paper, we conduct a systematic analysis of the construction thought for generating functions. We specifically examine the construction processes of specific algebraic forms, demonstrating their practical advantages through combinatorial counting problems. We extend the structural analysis of generating functions through the integration of Euler’s proof of the infinitude of primes. Furthermore, we interpret the Bertrand-Chebyshev theorem from the perspective of generating functions, highlighting how the absence of elementary contributions constrains the representational power of generating functions. Through an in-depth analysis of challenging sequence problems, we demonstrate the potential of generating functions in addressing complex mathematical problems. Finally, the future development of generating function construction thought is prospected, underscoring its indispensable role in modern mathematics and interdisciplinary fields.

Keywords

Construction Thought; Generating Functions; Representational Power; Sequence

References

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