Results 21 to 30 of about 1,866,320 (298)

Polynomial continued fractions [PDF]

Acta Arithmetica, 2002
Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one.
Bowman, Douglas, McLaughlin, James
openaire   +2 more sources

Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
doaj   +1 more source

The Reciprocal of a Continued Fraction [PDF]

Proceedings of the American Mathematical Society, 1952
Stieltjes [3, Chapter X],1 and later Rogers [2], gave formulas by means of which the reciprocal continued fractions for continued fractions of a certain class may be determined. We give below a theorem which extends the class of continued fractions to which this reciprocal transformation is applicable ;2 moreover, the theorem is stated in terms of ...
openaire   +2 more sources

Transcendental Continued Fractions

Communications in Mathematics, 2022
In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$
Ahallal, Sarra, Kacha, Ali
openaire   +4 more sources

Convergence criteria of branched continued fractions

Researches in Mathematics
The convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
doaj   +1 more source

On generalization of continued fraction of Gauss

International Journal of Mathematics and Mathematical Sciences, 1990
In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
doaj   +1 more source

Some properties of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2015
The fact that the values of the approximates of the positive definite branched continued fraction of special form are all in a certain circle is established for the certain conditions.
R.I. Dmytryshyn
doaj   +1 more source

Continued fraction solution linear differential equations [PDF]

, 1973
Murphy, JA, Drew, DM
core   +6 more sources

A Note on Continued Fractions [PDF]

Canadian Journal of Mathematics, 1960
Any real number y leads to a continued fraction of the type(1)where ai, bi are integers which satisfy the inequalities(2)by means of the algorithm(3)the a's being assigned positive integers. The process terminates for rational y; the last denominator bk satisfying bk ≥ ak + 1. For irrational y, the process does not terminate.
openaire   +2 more sources

ON SMARANDACHE GENERAL CONTINUED FRACTIONS [PDF]

, 1995
The continued fraction is called a Smarandache general continued fraction associated with A and ...
Maohua, Le
core   +1 more source