Arijit Jana

collaborators

2 papers

math.NT2020

Proof of a supercongruence conjecture of (F.3) of Swisher using the WZ-method

Arijit Jana, Gautam Kalita

For a non-negative integer $m$ , let $S (m)$ denote the sum given by $S (m) := n = 0 \sum m \frac{( - 1 ) ^{n} ( 8 n + 1 )}{n ! ^{3}} (\frac{1}{4})_{n}^{3} .$ Using the powerful WZ-method, for…

math.NT2020

Extension of a conjectural supercongruence of (G.3) of Swisher using Zeilberger's algorithm

Arijit Jana, Gautam Kalita

Using Zeilberger's algorithm, we here give a proof of the supercongruence $$ \sum_{n=0}^{\frac{p^r-3}{4}}(8n+1)\frac{\left(\frac{1}{4}\right)_n^4}{(1)_n^4}\equiv -p^3 \sum_{n=0}^{\…