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Generating k-Pell Infinite Series Using Whittaker’s Formula

In this paper, we apply Whittaker’s formula on 2 degree polynomial equations of the form: x + 2x – (k−1), where k≥ 2 and k∈ N. By applying Whittaker’s formula on these polynomial equations, we obtain infinite series for √k that involve integers belonging to specific k-Pell sequences. More specifically, the infinite series of √k will be made of terms containing the successive integers belonging to the k-Pell sequence {Pk−1,n}n.