Inequalities Involving $q$-Analogue of Multiple Psi Functions
نویسندگان
چکیده
منابع مشابه
ON A q-ANALOGUE OF THE MULTIPLE GAMMA FUNCTIONS
A q-analogue of the multiple gamma functions is introduced , and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function. 1 2 MICHITOMO NISHIZAWA
متن کاملq-ANALOGUE OF EULER-BARNES MULTIPLE ZETA FUNCTIONS
Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of higher order at negative integers. §
متن کاملMonotonicity of some functions involving the gamma and psi functions
Let L(x) := x − Γ(x+t) Γ(x+s) xs−t+1, where Γ(x) is Euler’s gamma function. We determine conditions for the numbers s, t so that the function Φ(x) := − Γ(x+t) xt−s−1 L′′(x) is strongly completely monotonic on (0, ∞). Through this result we obtain some inequalities involving the ratio of gamma functions and provide some applications in the context of trigonometric sum estimation. We also give se...
متن کاملSome Inequalities for the q-Analogue of the Classical Riemann Zeta Functions and the q-Polygamma Functions
We present the generalizations on some inequalities for the q-analogue of the classical Riemann zeta functions and the q-polygamma functions.
متن کاملInequalities Involving Generalized Bessel Functions
Let up denote the normalized, generalized Bessel function of order p which depends on two parameters b and c and let λp(x) = up(x), x ≥ 0. It is proven that under some conditions imposed on p, b, and c the Askey inequality holds true for the function λp , i.e., that λp(x) +λp(y) ≤ 1 +λp(z), where x, y ≥ 0 and z = x + y. The lower and upper bounds for the function λp are also established.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus. Mathématique
سال: 2020
ISSN: 1778-3569
DOI: 10.5802/crmath.44