Generalized Elliptic Integrals
By Ville Heikkala, Mavina Vamanamurthy, Matti Vuorinen. 2007
106 citations recorded by the source corpus.
Jacobi’s elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a quadrilateral and obtain sharp monotonicity and convexity properties for certain combinations of these integrals, thus generalizing analogous well-known results for classical conformal capacity and quasiconformal distortion functions. An algorithm for the computation of the modulus of the quadrilateral is given.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7d61ff10e47946c41750d1f91f755c5e8ab68167
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In Applied Mathematics
- 'Arp'ad Baricz
- Zhen-Hang Yang
- Jingfeng Tian
- Matti Vuorinen
- Ville Heikkala
- Mavina Vamanamurthy
- Sergei M. Sitnik
- Dmitrii Karp
In Geometry and Topology
- 'Arp'ad Baricz
- Zhen-Hang Yang
- Matti Vuorinen
- Mavina Vamanamurthy
- Ville Heikkala
- Sergei M. Sitnik
- Dmitrii Karp
- H. Lindén
Citations in the corpus
- Generalized elliptic integrals and the Legendre M-function (2007, methodology): “Proof. (1) By [ HVV , 3.17(7)] we know that the limit of f at r = 0 is (a + b − c)B(c,a + b − c)/B(a,b).”
- Log-convexity and log-concavity of hypergeometric-like functions (2009, background): “5. Acknowledgements. We thank Fedor Nazarov whose idea led to the proof of Theorem 1, ´ Arp´ad Baricz for providing us with the copies of [Baricz1, Baricz2, Ba ricz3, HVV, Bordelon] and many valuable comments, Matti Vuorinen for sharing the problem of log-concavity of 1F1 with us and Michael Gordy ”
- Turán type inequalities for hypergeometric functions (2008, background): “In [5, Theorem 2.14] we proved that the generalized complete elliptic integral [12] a (cid:4)→ K a,c ( r is log-convex, whenever 0 a min { c, 1 } and r ∈ (0 , 1) .”
- Convexity and monotonicity for elliptic integrals of the first kind and applications (2017, background): “Some of new generalizations can be found in [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40].”