Bounds for the product of modified Bessel functions
نویسندگان
چکیده
منابع مشابه
On a Product of Modified Bessel Functions
Let Iν and Kν denote the modified Bessel functions of the first and second kinds of order ν. In this note we prove that the monotonicity of u → Iν(u)Kν(u) on (0,∞) for all ν ≥ −1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order ν. Moreover, we show that the function u → Iν(u)Kν(u) is strict...
متن کاملUniform Bounds for Bessel Functions
For ν > −1/2 and x real we shall establish explicit bounds for the Bessel function Jν(x) which are uniform in x and ν. This work and the recent result of L. J. Landau [7] provide relatively sharp inequalities for all real x.
متن کاملRepresentation of the Modified Bessel Functions ∗
Some power series representations of the modified Bessel functions (McDonald functions Kα) are derived using the little known formalism of fractional derivatives. The resulting summation formulae are believed to be new. 1 Fractional derivatives There are several non-trivial examples in mathematics when some quantity, originally defined as integer, can radically extend its original range and ass...
متن کاملSome Inequalities for Modified Bessel Functions
We denote by Iν and Kν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function wν t t Iν−1 t /Iν t , t > 0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector 1984 , we establish new inequalities for Iν t /Iν−1 t . The results are based on the recurrence relations for Iν and Iν−1 and the ...
متن کاملLower Bounds for the Zeros of Bessel Functions
Let jp „ denote the nth positive zero of J , p > 0. Then / ■■> 7\'/2 Jp.n > Oln + P) ■ We begin by considering the eigenvalue problem (1) -(•*/)' + x~y = X2x2p-Xy, X,p>0, (2) y(a) =y(\) = 0, 0 < a < 1. For simplicity of notation we will set q = p~x. It is easily verified that the general solution of (1) is y(x) = CxJq(Xqxx/q) + C2Yq(Xqxx'q) and that the eigenvalues are given by Jq(Xq)Yq(Xqax/q)...
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: Aequationes mathematicae
سال: 2016
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-016-0414-2