Abramowitz, M. and Stegun, I. A. (Eds), Handbook of Mathematical Functions with Formu- las, Graphs, and Mathematical Tables(National Bureau of Standards, Applied Mathematics Series 55, 4th printing, with corrections, Washington, 1965).
Alzer, H. Inequalities for the volume of the unit ball in Rn, II, Mediterr. J. Math. 5 (4), –413, 2008.
Alzer, H. Sharp inequalities for the harmonic numbers, Expo. Math. 24 (4), 385–388, 2006.
Andrews, G. E., Askey, R. and Roy, R. Special Functions (Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge, 1999).
Atanassov, R. D. and Tsoukrovski, U. V. Some properties of a class of logarithmically com- pletely monotonic functions, C. R. Acad. Bulgare Sci. 41 (2), 21–23, 1988.
Batir, N. Inequalities for the gamma function, Arch. Math. 91, 554–563, 2008.
Batir, N. On some properties of digamma and polygamma functions, J. Math. Anal. Appl. (1), 452–465, 2007.
Batir, N. Some new inequalities for gamma and polygamma functions, J. Inequal. Pure Appl. Math. 6 (4), Art. 103, 2005.
(Available online at http://jipam.vu.edu.au/article.php?sid=577) Berg, C. Integral representation of some functions related to the gamma function, Mediterr. J. Math. 1 (4), 433–439, 2004.
Chen, Ch. -P. Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions, J. Math. Anal. Appl. 336, 812–822, 2007.
Chen, Ch. -P. and Qi, F. Logarithmically completely monotonic functions relating to the gamma function, J. Math. Anal. Appl. 321 (1), 405–411, 2006.
(Available online at http://dx.doi.org/10.1016/j.jmaa.2005.08.056).
Gautschi, W. The incomplete gamma function since Tricomi, in: Tricomi’s Ideas and Con- temporary Applied Mathematics(Atti Convegni Lincei 147, Accademia Nazionale dei Lincei, Rome, 1998), 203–237.
Grinshpan, A. Z. and Ismail, M. E. H. Completely monotonic functions involving the gamma and q-gamma functions, Proc. Amer. Math. Soc. 134, 1153–1160, 2006.
Koumandos, S. Monotonicity of some functions involving the gamma and psi functions, Math. Comp. 77, 2261–2275, 2008.
Mitrinovi´c, D. S., Peˇcari´c, J. E. and Fink, A. M. Classical and New Inequalities in Analysis (Kluwer, Dordrecht, 1993).
Qi, F. A completely monotonic function involving divided difference of psi function and an equivalent inequality involving sums, ANZIAM J. 48 (4), 523–532, 2007.
Qi, F. Three classes of logarithmically completely monotonic functions involving gamma and psi functions, Integral Transforms Spec. Funct. 18 (7), 503–509, 2007.
(Available online at http://dx.doi.org/10.1080/10652460701358976).
Qi, F. and Chen, Ch. -P. A complete monotonicity property of the gamma function, J. Math. Anal. Appl. 296 (2), 603–607, 2004.
(Available online at http://dx.doi.org/10.1016/j.jmaa.2004.04.026).
Qi, F. and Guo, B. -N. Some properties of the psi and polygamma functions, preprint. (Available online at http://arxiv.org/abs/0903.1003).
Qiu, S. -L. and Vuorinen, M. Some properties of the gamma and psi functions, with appli- cations, Math. Comp. 74 (250), 723–742, 2005.
Wang, Zh. -X. and Guo, D. -R. Special Functions (Translated from the Chinese by D.-R. Guo and X.-J. Xia, World Scientific Publishing, Singapore, 1989).
Widder, D. V. The Laplace Transform (Princeton University Press, Princeton, 1946).
Some Properties of the Psi and Polygamma Functions
Year 2010,
Volume: 39 Issue: 2, 219 - 231, 01.02.2010
Abramowitz, M. and Stegun, I. A. (Eds), Handbook of Mathematical Functions with Formu- las, Graphs, and Mathematical Tables(National Bureau of Standards, Applied Mathematics Series 55, 4th printing, with corrections, Washington, 1965).
Alzer, H. Inequalities for the volume of the unit ball in Rn, II, Mediterr. J. Math. 5 (4), –413, 2008.
Alzer, H. Sharp inequalities for the harmonic numbers, Expo. Math. 24 (4), 385–388, 2006.
Andrews, G. E., Askey, R. and Roy, R. Special Functions (Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge, 1999).
Atanassov, R. D. and Tsoukrovski, U. V. Some properties of a class of logarithmically com- pletely monotonic functions, C. R. Acad. Bulgare Sci. 41 (2), 21–23, 1988.
Batir, N. Inequalities for the gamma function, Arch. Math. 91, 554–563, 2008.
Batir, N. On some properties of digamma and polygamma functions, J. Math. Anal. Appl. (1), 452–465, 2007.
Batir, N. Some new inequalities for gamma and polygamma functions, J. Inequal. Pure Appl. Math. 6 (4), Art. 103, 2005.
(Available online at http://jipam.vu.edu.au/article.php?sid=577) Berg, C. Integral representation of some functions related to the gamma function, Mediterr. J. Math. 1 (4), 433–439, 2004.
Chen, Ch. -P. Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions, J. Math. Anal. Appl. 336, 812–822, 2007.
Chen, Ch. -P. and Qi, F. Logarithmically completely monotonic functions relating to the gamma function, J. Math. Anal. Appl. 321 (1), 405–411, 2006.
(Available online at http://dx.doi.org/10.1016/j.jmaa.2005.08.056).
Gautschi, W. The incomplete gamma function since Tricomi, in: Tricomi’s Ideas and Con- temporary Applied Mathematics(Atti Convegni Lincei 147, Accademia Nazionale dei Lincei, Rome, 1998), 203–237.
Grinshpan, A. Z. and Ismail, M. E. H. Completely monotonic functions involving the gamma and q-gamma functions, Proc. Amer. Math. Soc. 134, 1153–1160, 2006.
Koumandos, S. Monotonicity of some functions involving the gamma and psi functions, Math. Comp. 77, 2261–2275, 2008.
Mitrinovi´c, D. S., Peˇcari´c, J. E. and Fink, A. M. Classical and New Inequalities in Analysis (Kluwer, Dordrecht, 1993).
Qi, F. A completely monotonic function involving divided difference of psi function and an equivalent inequality involving sums, ANZIAM J. 48 (4), 523–532, 2007.
Qi, F. Three classes of logarithmically completely monotonic functions involving gamma and psi functions, Integral Transforms Spec. Funct. 18 (7), 503–509, 2007.
(Available online at http://dx.doi.org/10.1080/10652460701358976).
Qi, F. and Chen, Ch. -P. A complete monotonicity property of the gamma function, J. Math. Anal. Appl. 296 (2), 603–607, 2004.
(Available online at http://dx.doi.org/10.1016/j.jmaa.2004.04.026).
Qi, F. and Guo, B. -N. Some properties of the psi and polygamma functions, preprint. (Available online at http://arxiv.org/abs/0903.1003).
Qiu, S. -L. and Vuorinen, M. Some properties of the gamma and psi functions, with appli- cations, Math. Comp. 74 (250), 723–742, 2005.
Wang, Zh. -X. and Guo, D. -R. Special Functions (Translated from the Chinese by D.-R. Guo and X.-J. Xia, World Scientific Publishing, Singapore, 1989).
Widder, D. V. The Laplace Transform (Princeton University Press, Princeton, 1946).
Guo, B.-n., & Qi, F. (2010). Some Properties of the Psi and Polygamma Functions. Hacettepe Journal of Mathematics and Statistics, 39(2), 219-231.
AMA
Guo Bn, Qi F. Some Properties of the Psi and Polygamma Functions. Hacettepe Journal of Mathematics and Statistics. February 2010;39(2):219-231.
Chicago
Guo, Bai-ni, and Feng Qi. “Some Properties of the Psi and Polygamma Functions”. Hacettepe Journal of Mathematics and Statistics 39, no. 2 (February 2010): 219-31.
EndNote
Guo B-n, Qi F (February 1, 2010) Some Properties of the Psi and Polygamma Functions. Hacettepe Journal of Mathematics and Statistics 39 2 219–231.
IEEE
B.-n. Guo and F. Qi, “Some Properties of the Psi and Polygamma Functions”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, pp. 219–231, 2010.
ISNAD
Guo, Bai-ni - Qi, Feng. “Some Properties of the Psi and Polygamma Functions”. Hacettepe Journal of Mathematics and Statistics 39/2 (February 2010), 219-231.
JAMA
Guo B-n, Qi F. Some Properties of the Psi and Polygamma Functions. Hacettepe Journal of Mathematics and Statistics. 2010;39:219–231.
MLA
Guo, Bai-ni and Feng Qi. “Some Properties of the Psi and Polygamma Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, 2010, pp. 219-31.
Vancouver
Guo B-n, Qi F. Some Properties of the Psi and Polygamma Functions. Hacettepe Journal of Mathematics and Statistics. 2010;39(2):219-31.