Volume- 3
Issue- 3
Year- 2016
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D.A.GISMALLA , D.A.GISMALLA
In this survey , our aim is to represent to the reader a fascinating and a beautiful approach called Continued Fraction Technique (C.F.T.) to evaluate infinite series by transformation a series to its corresponding equivalent C.F. algorithm. First , We introduce the basic ideas of continued fraction to see how they arise out of high school division and also from solving equations .Second , theorems for Transformation infinite series to their equivalent C.F. are given .Some of these Transformation are to transform alternating series and series having an infinite product of terms. We observe one can use algebra to simplify the evaluations of the n-th continued fraction term to its equivalent one to generate the - transformation easily as in Theorem 2.3. Third , Matlab program software is written to compute some types of series efficiently. We , conclude with a computational remark showing the difficulties in computing some C.F. algorithms due to overflow or underflow for rounding errors , however this will not slamming C.F. for some types of certain problems it can't be avoided specially when evaluating Bessel's functions and its zeros or Hypergeometric series in [ 4] ,pp.272
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