Barkat Ali Bhayo and József Sándor

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 21, 2015, Number 2, Pages 1–7

**Full paper (PDF, 152 Kb)**

## Details

### Authors and affiliations

Barkat Ali Bhayo

*Department of Mathematical Information Technology, University of Jyväskylä
40014 Jyväskylä, Finland
*

József Sándor

*Babeș-Bolyai University, Department of Mathematics
Str. Kogălniceanu nr. 1, 400084 Cluj-Napoca, Romania
*

### Abstract

Here authors establish the sharp inequalities for classical beta function by studying the inequalities of trigonometric sine function

### Keywords

- Gamma function
- Beta function
- Sine function
- Jordan inequality

### AMS Classification

- 33B15
- 26D05
- 26D07
- 26D15

### References

- Abramowitz, M., & Stegun, I., eds. (1965) Handbook of Mathematical Functions with Formulas,Graphs and Mathematical Tables. National Bureau of Standards, Dover, New York.
- Alzer, H. (2003) Some beta function inequalities, Proc. of the Royal Soc. of Edinburgh, 133A, 731–745.
- Alzer, H. (1993) Some gamma function inequalities, Math. Comp., 60, 337–346.
- Alzer, H. (1997) On some inequalities for the gamma and psi functions, Math. Comp., 66,373–389.
- Anderson, G.D., Vamanamurthy, M.K., & Vuorinen, M. (1993) Inequalities of quasiconformal mappings in the space, Pacific J. Math., 160(1).
- Bhayo, B.A., & Sándor, J. (2014) On classical inequalities of trigonometric and hyperbolicfunctions, May 2014, http://arxiv.org/pdf/1405.0934.pdf.
- Andrews, G., Askey, R., & Roy, R. (1999) Special Functions, Encyclopedia of Mathematicsand its Applications, Vol. 71, Cambridge Univ. Press.
- Dragomir, S.S., Agarwal, R.P. & Barnett, N.S. (2000) Inequalities for beta and gamma functions via some classical and new integral inequalities, J. Inequal. Appl., 5, 103–165.
- Ivady, P. (2012) On a beta function inequality, J. Math. Inequal., 6(3), 333–341.
- Klen, R., Visuri, M., & Vuorinen, M. (2010) On Jordan type inequalities for hyperbolic functions, J. Ineq. Appl., Vol. 2010, Art. ID 362548, pp. 14.
- Mitrinovic, D.S. (1970) Analytic Inequalities, Springer-Verlag, Berlin.
- Neuman, E. & S´andor, J. (2010) On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities,Math. Inequal. Appl. 13(4), 715–723.
- Qiu, S.-L. & Vuorinen, M. (2004) Some properties of the gamma and psi functions withapplications, Math. Comp., 74(250), 723–742.
- Sándor, J. (2014) A bibliography on gamma functions: inequalities and applications, June 2014, Available online: http://www.math.ubbcluj.ro/jsandor/letolt/art42.pdf.
- Spanier, J. & Oldham, K.B. (1987) An atlas of functions, Hemisphere Publishing, Washington.

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## Cite this paper

Bhayo, B. A. & Sándor, J. (2015). On the inequalities for beta function. *Notes on Number Theory and Discrete Mathematics*, 21(2), 1-7.