Loading...
Please wait, while we are loading the content...
Similar Documents
Some inequalities for a hypergeometric integral
| Content Provider | Scilit |
|---|---|
| Author | Flett, T. M. |
| Copyright Year | 1972 |
| Description | In various problems in harmonic analysis (4, 5, 6), I have required an estimate for the integral for the hypergeometric function in the case where a>c−b>0, b>0, and 0 ≦ x < 1 (the integral is then unbounded as x→l−). Although there are innumerable identities for hypergeometric functions, few inequalities for these functions seem to be known, and in estimating the integral (1) I employed ad hoc arguments that made no use of the theory of hypergeometric functions. The estimates obtained were adequate for my purposes, but were far from sharp, and the object of this note is to show that, by assembling a few known facts concerning hypergeometric functions, we can obtain sharp inequalities for the integral (1). We also give (in §4) several related inequalities that can be obtained by transforming the integral. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F84F2622C9D96B9B56540371A78DBD6E/S0013091500026122a.pdf/div-class-title-some-inequalities-for-a-hypergeometric-integral-div.pdf |
| Ending Page | 34 |
| Page Count | 4 |
| Starting Page | 31 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s0013091500026122 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 1 |
| Volume Number | 18 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1972-06-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society Applied Mathematics Hypergeometric Functions |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
