# A New Result in Form of Finite Triple Sums for a Series from Ramanujan’s Notebooks

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Test of Validity

## 4. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The seven possibilities to construct trees with four labelled nodes and one improper edge.

**Figure 2.**The top arrays display values of ${\rho}_{r,j,k}$ for the cases with $r=3$ (

**left**), $r=4$ (

**middle**) and $r=5$ (

**right**). The bottom arrays show the resulting quotients upon division by binomials on the form “$2r-j$ over $k$”. The colored numbers are referenced in the text.

**Figure 4.**(

**Left**) LHS of Equation (5) (orange), RHS of Equation (5) (black dashed) and computed LHS of Equation (1) (blue points) for $x=1.9$, $r=10$ and varying $u$. (

**Right**) Region of complex plane, where the series on the LHS of Equation (1) converges and where Equation (1) holds true (see Equation (11)).

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**MDPI and ACS Style**

Vigren, E.; Dieckmann, A.
A New Result in Form of Finite Triple Sums for a Series from Ramanujan’s Notebooks. *Symmetry* **2022**, *14*, 1090.
https://doi.org/10.3390/sym14061090

**AMA Style**

Vigren E, Dieckmann A.
A New Result in Form of Finite Triple Sums for a Series from Ramanujan’s Notebooks. *Symmetry*. 2022; 14(6):1090.
https://doi.org/10.3390/sym14061090

**Chicago/Turabian Style**

Vigren, Erik, and Andreas Dieckmann.
2022. "A New Result in Form of Finite Triple Sums for a Series from Ramanujan’s Notebooks" *Symmetry* 14, no. 6: 1090.
https://doi.org/10.3390/sym14061090