Landen Inequalities for Zero-Balanced Hypergeometric Functions
For zero-balanced Gaussian hypergeometric functions F(a,b;a+b;x), a,b>0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x∈(0,1). Thereby an exhausting answer is given t...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/932061 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850216685255000064 |
|---|---|
| author | Slavko Simić Matti Vuorinen |
| author_facet | Slavko Simić Matti Vuorinen |
| author_sort | Slavko Simić |
| collection | DOAJ |
| description | For zero-balanced Gaussian hypergeometric functions F(a,b;a+b;x), a,b>0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x∈(0,1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990. |
| format | Article |
| id | doaj-art-36154fdc2d934a719ae00962c8ef3ade |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-36154fdc2d934a719ae00962c8ef3ade2025-08-20T02:08:14ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/932061932061Landen Inequalities for Zero-Balanced Hypergeometric FunctionsSlavko Simić0Matti Vuorinen1Mathematical Institute, SANU, Kneza Mihaila 36, 11000 Belgrade, SerbiaDepartment of Mathematics, University of Turku, 20014 Turku, FinlandFor zero-balanced Gaussian hypergeometric functions F(a,b;a+b;x), a,b>0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x∈(0,1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.http://dx.doi.org/10.1155/2012/932061 |
| spellingShingle | Slavko Simić Matti Vuorinen Landen Inequalities for Zero-Balanced Hypergeometric Functions Abstract and Applied Analysis |
| title | Landen Inequalities for Zero-Balanced Hypergeometric Functions |
| title_full | Landen Inequalities for Zero-Balanced Hypergeometric Functions |
| title_fullStr | Landen Inequalities for Zero-Balanced Hypergeometric Functions |
| title_full_unstemmed | Landen Inequalities for Zero-Balanced Hypergeometric Functions |
| title_short | Landen Inequalities for Zero-Balanced Hypergeometric Functions |
| title_sort | landen inequalities for zero balanced hypergeometric functions |
| url | http://dx.doi.org/10.1155/2012/932061 |
| work_keys_str_mv | AT slavkosimic landeninequalitiesforzerobalancedhypergeometricfunctions AT mattivuorinen landeninequalitiesforzerobalancedhypergeometricfunctions |