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Some properties of the psi function and evaluations of γ
Applied Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Song-Liang Qiu
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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.
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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.
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On proofs for monotonicity of a function involving the psi and exponential functions
Analysis (Germany), 2013The authors give two simple proofs of the known fact that the function \[ \psi(x)+\ln(e^{1/x}-1) \] is strictly increasing on \((0,+\infty)\). Here, \(\psi(x)\) is the logarithmic derivative of the Euler gamma function, also known as the digamma function.
Wen-Hui Li, Feng Qi, Bai-Ni Guo
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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.
Guennadi Kozlov +2 more
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Multipoint Padé Approximation of the Psi Function
Mathematical Notes, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A formula for the Chebyshev PSI function
Mathematical Notes of the Academy of Sciences of the USSR, 1978A formula expressing the Chebyshevψ function in terms of the characteristic values of the Laplace-Beltrami operator on the fundamental domain of a modular group and the hyperbolic classes of conjugate elements of this group is derived.
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INEQUALITIES INVOLVING GAMMA AND PSI FUNCTIONS
Analysis and Applications, 2003We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove that (xmψ(x))(m+1) is completely monotonic. We conjecture that -(xmψ(m)(x))(m) is completely monotonic for m ≥ 2; and we prove it, with help from Maple, for 2 ≤ m ≤ 16. We give a very useful Maple procedure to verify this for higher values of m.
Clark, W. Edwin, Ismail, Mourad E. H.
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On $$(\phi ,\psi )$$-Inframonogenic Functions in Clifford Analysis
Bulletin of the Brazilian Mathematical Society, New Series, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel Alfonso Santiesteban +2 more
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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.
Thomas Kappeler, Jürgen Pöschel
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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.
Thomas Kappeler, Jürgen Pöschel
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Rendiconti del Circolo Matematico di Palermo, 2009
S. J. Taylor has introduced the idea of \(\psi\)-density which is stronger than the usual Lebesgue density function by replacing the entity \(2h\) in the denominator in the definition of Lebesgue density by the entity \(2h.\psi(2h)\) where \(\psi :(0, \infty) \rightarrow (0, \infty)\) is a nondecreasing continuous function with \(\lim_{t \rightarrow 0^+
Filipczak, Małgorzata +1 more
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S. J. Taylor has introduced the idea of \(\psi\)-density which is stronger than the usual Lebesgue density function by replacing the entity \(2h\) in the denominator in the definition of Lebesgue density by the entity \(2h.\psi(2h)\) where \(\psi :(0, \infty) \rightarrow (0, \infty)\) is a nondecreasing continuous function with \(\lim_{t \rightarrow 0^+
Filipczak, Małgorzata +1 more
openaire +2 more sources