Sums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional CalculusSums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional Calculus

An attempt is made here to introduce and study a pair of double power series associated with the generalized zeta function due to Erdélyi Φ(x; z; a) together with related sums, integral representations, generating relations and N-fractional calculus. A number of (known and new) results shown to follow as special cases of our theorems.