Abstract
In this paper, we exhibit short deductions of the Jha and Malenfant expressions for the partition function, and we show several connections between the Euler, divisor and partition functions via the partial Bell polynomials and Hessenberg determinants. Besides, we show that the Gandhi's recurrence relation for colour partitions implies the Osler-Hassen-Chandrupatla's expression for the divisor function.
| Original language | English |
|---|---|
| Pages (from-to) | 1-9 |
| Number of pages | 9 |
| Journal | Proceedings of the Jangjeon Mathematical Society |
| Volume | 26 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2023 |
Keywords
- Bell polynomials
- Colour partitions
- Hessenberg determinant
- Malenfant and Jha formulas
- Partition function
- Sum of divisors function
- q-analysis