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Category: Analysis

Summation Chains of Sequences Part 3: Sequence Chains from Linear Functions

Summation Chains of Sequences Part 3: Sequence Chains from Linear Functions

For the full paper, which includes proofs, click here. Abstract (Editor's note:) This paper represents the third installment of a masters thesis by Jonathan Johnson. The first two can be found here and here. This paper continues the development of the theory of summation chains of sequences. Since summation chains are doubly infinite, it's important to know how little…

Summation Chains of Sequences Part 2: Relationships between Sequences via Summation Chains

Summation Chains of Sequences Part 2: Relationships between Sequences via Summation Chains

For the full paper with proofs,click here. Abstract Editor's note: This paper represents the second installment of a masters thesis by Jonathan Johnson. This paper continues the development of the theory of summation chains of sequences. The concept of sum-related is defined: two sequences are sum-related if one sequence appears in the summation chain of the…

Summation Chains of Sequences Part 1: Introduction, Generation, and Key Definitions

Summation Chains of Sequences Part 1: Introduction, Generation, and Key Definitions

For the full paper, which includes all proofs, download the pdf here Abstract (Editor's note:) This paper represents the first installment of a masters thesis by Jonathan Johnson. This work introduces the notion of summation chains of sequences. It examines the sequence of sequences generated by partial sums and differences of terms in each level of…