A general form of Jordan-type double inequality for the generalized and normalized Bessel functions

作者：Zhu, Ling^*

来源：Applied Mathematics and Computation, 2010, 215(11): 3802-3810.

DOI：10.1016/j.amc.2009.11.020

• Lower and upper bounds
• Best constant
• A general form of Jordan-type double inequality
• The generalized and normalized Bessel functions
• The Spherical Bessel Functions (SBFs)
• The SBFs of the first kind j(n)(x) = root pi/2x J(n+1/2)(x)
• The Modified Spherical Bessel Functions (MSBFs)
• The MSBFs of the first kind i(n)(x) = root pi/2x In+1/2(x)
• Two new infinite series for sin x/x and sinh x/x

In this note, a general form of Jordan-type double inequality involving the generalized and normalized Bessel functions is presented, and then some recent results concerning generalized and sharp work of Jordan's inequality are extended. At the same time, the applications of the results above give two new infinite series for sin x/x and sinh x/x.

• 出版日期2010-2-1
• 单位浙江工商大学