Hypergeometric Functions and Hyperbolic Metric

Anderson, G. D.; Sugawa, Toshiyuki; Vamanamurthy, M. K.; Вуоринен, Матти

doi:10.1007/bf03321727

Search citation statements

Order By: Relevance

Paper Sections

Select...

Preliminaries1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with Ψ(x) = Γ ′ (x)/Γ(x) being the digamma function. The asymptotic formula in (2.5) for the case a + b = c is due to Ramanujan, see [1,3].…”

Section: Preliminariesmentioning

confidence: 99%

Asymptotic Properties of the Hyperbolic Metric on the Sphere With Three Conical Singularities

Zhang¹

2014

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. The explicit formula for the hyperbolic metric λ α, β, γ (z)|dz| on the thrice-punctured sphere P\{0, 1, ∞} with singularities of order 0 < α, β < 1, γ ≤ 1, α + β + γ > 2 at 0, 1, ∞ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of λ α, β, γ (z) near the origin and give more precise descriptions for the asymptotic behavior of λ α, β, γ (z).

show abstract

“…with Ψ(x) = Γ ′ (x)/Γ(x) being the digamma function. The asymptotic formula in (2.5) for the case a + b = c is due to Ramanujan, see [1,3].…”

Section: Preliminariesmentioning

confidence: 99%

Asymptotic Properties of the Hyperbolic Metric on the Sphere With Three Conical Singularities

Zhang¹

2014

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

Hypergeometric Functions and Hyperbolic Metric

Abstract: Abstract. We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

Cited by 1 publication

References 15 publications

Asymptotic Properties of the Hyperbolic Metric on the Sphere With Three Conical Singularities

Asymptotic Properties of the Hyperbolic Metric on the Sphere With Three Conical Singularities

Contact Info

Product

Resources

About