The function Yν is sometimes called a Bessel function of the second kind.2 The key point of the current discussion is that a well-defined mathematical procedure has been used to define a second solution to the Bessel ODE, so that for a given value of the parameter n2 in that ODE, the...
By use of a computer and Mathematicathe elementary function cos x is visualized as a limit of the graphs of Taylor polynomials. A slight modification of the Taylor polynomials for cos xleads to a computer visualization of the graph of the Bessel function J0 (x).By similar modifications the ...
The function to accomplish this in Mathematica is: To test the accuracy of these solutions, we evaluate each extremum into the derivative of the Bessel function, Eqn. (1), to determine if it is a root. Evaluating every extremum, Jn′(en,m), the error is not more than the stated accura...
New function BesselJZero has been added to the built-in Mathematica kernel.New function BesselYZero has been added to the built-in Mathematica kernel. Evaluate the 5 th zero of the Bessel function numerically: Version 5.2 In[1]:= Out[1]= ...
By use of a computer and Mathematica the elementary function cos x is visualized as a limit of the graphs of Taylor polynomials. A slight modification of the Taylor polynomials for cos x leads to a computer visualization of the graphs of the Bessel function Jo(x) . By similar modifications ...
Acta Mathematica HungaricaL. LORCH AND P. SZEGO, A singular integral whose kernel involves a Bessel function, Duke Math. J. 22 (1955). 407418.A singular integral whose kernel involves a Bessel function - Lorch, Szego - 1955 () Citation Context ...e Bessel function of order ν of the ...
We denote by and the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function , , in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector (1984), we establ
Bessel (Riesz) Potentials on Banach Function Spaces and Their Applications Ⅰ Theory. Acta Mathematica Sinica, 1998, 14(3): 327-340 https://doi.org/10.1007/BF02580436 上一篇 下一篇 参考文献 [1] Lindenstrauss J,Tzafriri L.Classical Banach Spaces Ⅱ.Berlin,Heidelberg,New York:Springer-Verl...
We denote by and the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function , , in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector (1984), we establ
( Department of Mathematics , Hebei University , Baoding 071002 , China)Abstract In this paper , we shall introduce the notion of the Bessel ( Riesz) potentialK¨ othe function spaces Xs( Xs) and give some dual estimates for a class of operators de2termined by a semi - group in the ...