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In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.doi:10.1080/10652460600725234 fatcat:in2tmgwxovfmnozdzy2x6kqanm