New Inequalities for Nielsen’s Beta Function
نویسندگان
چکیده
منابع مشابه
Inequalities for the Beta function
Let g(x) := (e/x)xΓ(x+ 1) and F(x,y) := g(x)g(y)/g(x + y) . Let D x,y be the k th differential in Taylor’s expansion of logF(x,y) . We prove that when (x,y) ∈ R+ one has (−1)k−1D x,y (X ,Y ) > 0 for every X ,Y ∈ R+ , and that when k is even the conclusion holds for every X ,Y ∈ R with (X ,Y ) = (0,0) . This implies that Taylor’s polynomials for logF provide upper and lower bounds for logF accor...
متن کاملNew integral inequalities for $s$-preinvex functions
In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.
متن کاملNew inequalities for a class of differentiable functions
In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.
متن کاملInequalities for Gamma Function Ratios
Write R(x, y) = Γ(x + y) Γ(x). Inequalities for this ratio have interesting applications, and have been considered by a number of writers over a long period. In a Monthly article [7], Wendel showed that x(x + y) y−1 ≤ R(x, y) ≤ x y for 0 ≤ y ≤ 1. (1) Wendel's method was an ingenious application of Hölder's inequality to the integral definition of the gamma function. Note that both inequalities ...
متن کاملQuadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|
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: Communications in Mathematics and Applications
سال: 2019
ISSN: 0976-5905,0975-8607
DOI: 10.26713/cma.v10i4.1233