Results 291 to 300 of about 355,849 (306)
Some of the next articles are maybe not open access.
2003
In this appendix we prove the following theorem stated in section 8. In the form presented it is due to [6], but the proof given here is much simpler, and the normalizing constants are explicitly computed. See also [90] for prior results. — For notations we refer to sections 6 and 7.
Jürgen Pöschel, Thomas Kappeler
openaire +2 more sources
In this appendix we prove the following theorem stated in section 8. In the form presented it is due to [6], but the proof given here is much simpler, and the normalizing constants are explicitly computed. See also [90] for prior results. — For notations we refer to sections 6 and 7.
Jürgen Pöschel, Thomas Kappeler
openaire +2 more sources
Journal of Difference Equations and Applications, 2001
To the author's knowledge, among the so—called special functions, the gamma function is a unique one which is defined by a linear difference equation and is a hyper—transcendental function. There exists an another well—known hyper—transcendental function called the psi function, which is merely the logarithmic derivative of the gamma function.
openaire +2 more sources
To the author's knowledge, among the so—called special functions, the gamma function is a unique one which is defined by a linear difference equation and is a hyper—transcendental function. There exists an another well—known hyper—transcendental function called the psi function, which is merely the logarithmic derivative of the gamma function.
openaire +2 more sources
Insights into function of PSI domains from structure of the Met receptor PSI domain
Biochemical and Biophysical Research Communications, 2004PSI domains are cysteine-rich modules found in extracellular fragments of hundreds of signaling proteins, including plexins, semaphorins, integrins, and attractins. Here, we report the solution structure of the PSI domain from the human Met receptor, a receptor tyrosine kinase critical for proliferation, motility, and differentiation.
Kozlov, Guennadi +6 more
openaire +4 more sources
Continued Fractions for the PSI Function and Its Derivatives
SIAM Journal on Applied Mathematics, 1971It is shown that the series part of higher derivatives of the logarithm of the gamma function can be expressed as a Stieltjes transform. This leads to continued fraction developments of Stieltjes type and J-fraction form. The first few terms in the fractions are given for some of the lower derivatives, and a few partial quotients are derived in the ...
L. R. Shenton, Kimiko o Bowman
openaire +2 more sources
Estimations of psi function and harmonic numbers
Applied Mathematics and Computation, 2015The asymptotic expansion of digamma function is a starting point for the derivation of approximants for harmonic sums or Euler-Mascheroni constant. It is usual to derive such approximations as values of logarithmic function, which leads to the expansion of the exponentials of digamma function.
openaire +2 more sources
Monotonicity properties of functions related to the psi function
Applied Mathematics and Computation, 2010Abstract In this paper, the monotonicity properties of functions related to the psi function are obtained, a double inequality for the Euler–Mascheroni constant is established. Relevant connections of the results presented here with those derived in earlier works are also pointed out.
openaire +2 more sources
Some properties of functions related to the gamma and psi functions
Integral Transforms and Special Functions, 2010In this paper, several properties associated with the complete monotonicity, the strongly complete monotonicity and the logarithmically complete monotonicity of functions related to the gamma and psi functions are obtained. Relevant connections of the results presented here with those derived in earlier works are also pointed out.
Feng Qi +2 more
openaire +2 more sources
Continued fraction estimates for the psi function
Applied Mathematics and Computation, 2013We present continued fraction estimates for the psi function. As a consequence, we educe inequality for the Euler-Mascheroni constant, which improves a result of DeTemple.
openaire +2 more sources
Accurate Estimates of the Gamma Function Involving the PSI Function
Numerical Functional Analysis and Optimization, 2011The main result of this article is to establish new and accurate approximations of the gamma function in terms of the digamma function, that improve a result of Alzer and Batir [Appl. Math. Lett. 20(2007):778–781].
openaire +2 more sources
The Gamma, Beta, Pi, and Psi Functions
1995Publisher Summary This chapter discusses the gamma, beta, pi, and psi functions. The gamma function, denoted by Γ(x), provides a generalization of n factorial n to the case in which n is not an integer. It is defined by the Euler integral. The chapter presents the special function of Γ(x) and the gamma function in the complex plane.
openaire +2 more sources