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  • 1 Department of Mathematics and Computer Science Faculty of Science and Technology, Prince of Songkla University Pattani Campus 94000, Thailand Pattani Campus 94000, Thailand
  • | 2 Department of Mathematics, Faculty of Science, Kasetsart University Bangkok 10900, Thailand Bangkok 10900, Thailand
  • | 3 Department of Mathematics, Faculty of Science, Chulalongkorn University Bangkok 10330, Thailand Bangkok 10330, Thailand
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Summary  

Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method. The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization. Similar results are also established for continued fractions in the field of formal series over a finite base field.

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