a bibliography of gamma function and related … · a bibliography of gamma function and related...

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A BIBLIOGRAPHY OF GAMMA FUNCTION AND RELATED TOPICS Version 0.4. – January 2010, http://milanmerkle.com References [1] Ibrahim A. Abou Tair. On certain Dirichlet series related to Hurwitz Zeta-function. J. Inst. Math. Comput. Sci. Math. Ser. [Journal of Institute of Mathematics and Computer Sciences (Mathematics Series)] 3(3):299–304, 1990. [2] Jorge Alberto Achcar, Heleno Bolfarine. The log-linear model with a generalized Gamma distribution for the error: A Bayesian approach. Statist. Probab. Lett. [Statistics and Prob- ability Letters] 4(6):325–332, 1986. [3] V. S. Adamchik, O. I. Marichev. Representations of functions of hypergeometric type in logarithmic cases. Vestsi Akad. Navuk BSSR Ser. Fiz. Mat. Navuk [Vestsi Akademii Navuk BSSR. Seryya Fizika Matematychnykh Navuk](5):29–35, 1983. In Russian. [4] A. Adatia, A. G. Law, Q. Wang. Characterization of a mixture of Gamma distributions via conditional finite moments. Comm. Statist. Theory Methods [Communications in Statistics. Theory and Methods] 20(5–6):1937–1949, 1991. [5] I. I. Adgamov, I. N. Volodin. On a test for the Weibull distribution against a family of gener- alized Gamma-alternatives. Izv. Vyssh. Uchebn. Zaved. Mat. [Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika](6):3–8, 90, 1987. Russian. [6] C. Adiga, T. Kim. On a generalization of S´andor’s function. Proc. Jangjeon Math. Soc. 5(2):121–124, 2002. [7] C. Adiga et al. On a q-analogue of S´andor’s function. J. Ineq. Pure Appl. Math. 4(5), 2003. art.84 (electronic). [8] Alan Adolphson. Uniqueness of γp in the Gross-Koblitz formula for Gauss sums. Trans. Amer. Math. Soc. [Transactions of the American Mathematical Society] 278(1):57–63, 1983. [9] A.U. Afuwape, C.O. Imoru. Bounds for the Beta function. Bolletino U.M.I. 5(17-A):330– 334, 1980. [10] R.P. Agarwal. Difference equations and inequalities. Marcel Dekker, Inc., 2nd edition, 2000. [11] Abdul Hadi Nabih Ahmed, A. M. Abouammoh. Characterizations of Gamma, inverse Gauss- ian, and negative binomial distributions via their length-biased distributions. Statist. Papers [Statistical Papers. Statistische Hefte] 34(2):167–173, 1993. [12] A. M. Al Rashed, S. I. Ahmed. A generalization of the number π. J. Natur. Sci. Math. [The Journal of Natural Sciences and Mathematics] 29(1):29–37, 1989. [13] M. Masoom Ali, A. K. Md. E. Saleh, Dale Umbach. Estimating functions of location and scale parameters. Soochow J. Math. [Soochow Journal of Mathematics] 19(3):259–270, 1993. [14] A. Alikhani, M. Hassani. Approximation of pn by hn. RGMIA Research Report Collection 8(4), 2005. [15] Giampietro Allasia, Renata Besenghi. Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. [Numerische Mathematik] 50(4):419–428, 1987. [16] Giampietro Allasia, Renata Besenghi. Numerical calculation of the Gamma and Digamma functions using the trapezoidal rule. Boll. Un. Mat. Ital. B (7) [Unione Matematica Italiana. Bollettino. B. Serie-VII] 1(3):815–828, 1987. Italian. [17] J.P. Allouche. Transcendence of the Carlitz-Goss Gamma function at rational arguments. J. Number Theory 60(2):318–328, 1996. [18] C. Alsina, M.S. Tom´as. A geometrical proof of a new inequality for the Gamma function. J. Ineq. Pure Appl. Math. 6(2), 2005. [19] A.A. Alyakrinskii. On the representation of the values of Euler’s Gamma function at some rational points in the form of an infinite product. In Investigations in complex analysis (Russian), 123–128. Krasnoyarsk. Gos. Univ., 1989. [20] H. Alzer. On some inequalities involving (n!) 1/n , II. Period. Math. Hung. 28(3):229–233, 1994. [21] H. Alzer. Note on an inequality involving (n!) 1/n . Acta Math. Univ. Comen. New Ser. 64:283–285, 1995. [22] H. Alzer. Characterizations of the ratio of Gamma and q-Gamma functions. Abh. Math. Sem. Univ. Hamburg 70:165–174, 2000. [23] H. Alzer. Inequalities for the Gamma function. Proc. Amer. Math. Soc. 128:141–147, 2000. 1

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Page 1: A BIBLIOGRAPHY OF GAMMA FUNCTION AND RELATED … · A BIBLIOGRAPHY OF GAMMA FUNCTION AND RELATED TOPICS Version 0.4. { January 2010, References [1] Ibrahim A. Abou Tair. On certain

A BIBLIOGRAPHY OF GAMMA FUNCTION AND RELATED TOPICS

Version 0.4. – January 2010, http://milanmerkle.com

References

[1] Ibrahim A. Abou Tair. On certain Dirichlet series related to Hurwitz Zeta-function. J. Inst.

Math. Comput. Sci. Math. Ser. [Journal of Institute of Mathematics and Computer Sciences

(Mathematics Series)] 3(3):299–304, 1990.[2] Jorge Alberto Achcar, Heleno Bolfarine. The log-linear model with a generalized Gamma

distribution for the error: A Bayesian approach. Statist. Probab. Lett. [Statistics and Prob-

ability Letters] 4(6):325–332, 1986.[3] V. S. Adamchik, O. I. Marichev. Representations of functions of hypergeometric type in

logarithmic cases. Vestsi Akad. Navuk BSSR Ser. Fiz. Mat. Navuk [Vestsi Akademii Navuk

BSSR. Seryya Fizika Matematychnykh Navuk](5):29–35, 1983. In Russian.[4] A. Adatia, A. G. Law, Q. Wang. Characterization of a mixture of Gamma distributions via

conditional finite moments. Comm. Statist. Theory Methods [Communications in Statistics.

Theory and Methods] 20(5–6):1937–1949, 1991.[5] I. I. Adgamov, I. N. Volodin. On a test for the Weibull distribution against a family of gener-

alized Gamma-alternatives. Izv. Vyssh. Uchebn. Zaved. Mat. [Izvestiya Vysshikh UchebnykhZavedenii. Matematika](6):3–8, 90, 1987. Russian.

[6] C. Adiga, T. Kim. On a generalization of Sandor’s function. Proc. Jangjeon Math. Soc.

5(2):121–124, 2002.[7] C. Adiga et al. On a q-analogue of Sandor’s function. J. Ineq. Pure Appl. Math. 4(5), 2003.

art.84 (electronic).

[8] Alan Adolphson. Uniqueness of γp in the Gross-Koblitz formula for Gauss sums. Trans.Amer. Math. Soc. [Transactions of the American Mathematical Society] 278(1):57–63, 1983.

[9] A.U. Afuwape, C.O. Imoru. Bounds for the Beta function. Bolletino U.M.I. 5(17-A):330–

334, 1980.[10] R.P. Agarwal. Difference equations and inequalities. Marcel Dekker, Inc., 2nd edition, 2000.

[11] Abdul Hadi Nabih Ahmed, A. M. Abouammoh. Characterizations of Gamma, inverse Gauss-

ian, and negative binomial distributions via their length-biased distributions. Statist. Papers[Statistical Papers. Statistische Hefte] 34(2):167–173, 1993.

[12] A. M. Al Rashed, S. I. Ahmed. A generalization of the number π. J. Natur. Sci. Math. [TheJournal of Natural Sciences and Mathematics] 29(1):29–37, 1989.

[13] M. Masoom Ali, A. K. Md. E. Saleh, Dale Umbach. Estimating functions of location and

scale parameters. Soochow J. Math. [Soochow Journal of Mathematics] 19(3):259–270, 1993.[14] A. Alikhani, M. Hassani. Approximation of pn by hn. RGMIA Research Report Collection

8(4), 2005.

[15] Giampietro Allasia, Renata Besenghi. Numerical calculation of incomplete gamma functionsby the trapezoidal rule. Numer. Math. [Numerische Mathematik] 50(4):419–428, 1987.

[16] Giampietro Allasia, Renata Besenghi. Numerical calculation of the Gamma and Digamma

functions using the trapezoidal rule. Boll. Un. Mat. Ital. B (7) [Unione Matematica Italiana.Bollettino. B. Serie-VII] 1(3):815–828, 1987. Italian.

[17] J.P. Allouche. Transcendence of the Carlitz-Goss Gamma function at rational arguments.

J. Number Theory 60(2):318–328, 1996.[18] C. Alsina, M.S. Tomas. A geometrical proof of a new inequality for the Gamma function.

J. Ineq. Pure Appl. Math. 6(2), 2005.

[19] A.A. Alyakrinskii. On the representation of the values of Euler’s Gamma function at somerational points in the form of an infinite product. In Investigations in complex analysis

(Russian), 123–128. Krasnoyarsk. Gos. Univ., 1989.

[20] H. Alzer. On some inequalities involving (n!)1/n, II. Period. Math. Hung. 28(3):229–233,1994.

[21] H. Alzer. Note on an inequality involving (n!)1/n. Acta Math. Univ. Comen. New Ser.

64:283–285, 1995.[22] H. Alzer. Characterizations of the ratio of Gamma and q-Gamma functions. Abh. Math.

Sem. Univ. Hamburg 70:165–174, 2000.[23] H. Alzer. Inequalities for the Gamma function. Proc. Amer. Math. Soc. 128:141–147, 2000.

1

Page 2: A BIBLIOGRAPHY OF GAMMA FUNCTION AND RELATED … · A BIBLIOGRAPHY OF GAMMA FUNCTION AND RELATED TOPICS Version 0.4. { January 2010, References [1] Ibrahim A. Abou Tair. On certain

2 Bibliography of Gamma function–v.0.4 (January 2010) http://milanmerkle.com

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