Page 1 Next

## Displaying 1 – 20 of 169

Showing per page

### 3x+1 inverse orbit generating functions almost always have natural boundaries

Acta Arithmetica

The 3x+k function ${T}_{k}\left(n\right)$ sends n to (3n+k)/2, resp. n/2, according as n is odd, resp. even, where k ≡ ±1 (mod 6). The map ${T}_{k}\left(·\right)$ sends integers to integers; for m ≥1 let n → m mean that m is in the forward orbit of n under iteration of ${T}_{k}\left(·\right)$. We consider the generating functions ${f}_{k,m}\left(z\right)={\sum }_{n>0,n\to m}{z}^{n}$, which are holomorphic in the unit disk. We give sufficient conditions on (k,m) for the functions ${f}_{k,m}\left(z\right)$ to have the unit circle |z|=1 as a natural boundary to analytic continuation. For the 3x+1 function these conditions hold for all m...

### 5-dissections and sign patterns of Ramanujan's parameter and its companion

Czechoslovak Mathematical Journal

In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction $R\left(q\right)$ and its reciprocal. We obtain the 5-dissections for functions $R\left(q\right)R{\left({q}^{2}\right)}^{2}$ and $R{\left(q\right)}^{2}/R\left({q}^{2}\right)$, which are essentially Ramanujan’s parameter and its companion. Additionally, 5-dissections of the reciprocals of these two functions are derived. These 5-dissection formulas imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.

### A class of starlike mappings of the unit disk

Compositio Mathematica

### A curious property of series involving terms of generalized sequences.

International Journal of Mathematics and Mathematical Sciences

### A Disproof of a Conjecture of Robertson and Generalizations

Publications de l'Institut Mathématique

### A gap series with growth conditions and its applications.

Mathematica Scandinavica

### A hybrid of Darboux's method and singularity analysis in combinatorial asymptotics.

The Electronic Journal of Combinatorics [electronic only]

### A majorant problem.

International Journal of Mathematics and Mathematical Sciences

### A probabilistic description of the three theorems of Hardy.

Southwest Journal of Pure and Applied Mathematics [electronic only]

### A ridiculously simple and explicit implicit function theorem.

Séminaire Lotharingien de Combinatoire [electronic only]

### A Vanishing Theorem for Power Series.

Inventiones mathematicae

### Absolutely convergent series expansions for quasi periodic motions.

Mathematical Physics Electronic Journal [electronic only]

### Accelerating the Convergence of Power Series of Certain Entire Functions.

Numerische Mathematik

### An application of Kronecker' s theorem to rational functions.

Mathematische Annalen

### An area inequality for quasi-subordinate analytic functions

Annales Polonici Mathematici

Integers

### An extension of a theorem of Abian

Archivum Mathematicum

### An inequality for univalent functions due to Dvořák

Časopis pro pěstování matematiky

### Applications of a special representation of analytic functions.

Southwest Journal of Pure and Applied Mathematics [electronic only]

### Approximation of entire functions of slow growth.

General Mathematics

Page 1 Next