Integral representations for binomial sums of chances of winning
Addona, Wagon and Wilf (Ars Math. Contemp. 4 (1) (2011), 29-62) examined a problem about the winning chances in tossing unbalanced coins. Here we present some integral representations associated with such winning probabilities in a more general setting via using certain Fourier transform method. When our newly introduced parameters (r, d) are set to be (0, 1), one of our results reduces to the main formula in the above reference.
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