# bessel function in a sentence

### Examples

- Inside the spheres, they can be any smooth continuation, such as a linear combination of polynomials or
*Bessel functions*. - The
*Bessel function*of the second kind then can be thought to naturally appear as the imaginary part of the Hankel functions. - The
*Bessel functions*are valid even for complex arguments, and an important special case is that of a purely imaginary argument. - For instance, the Sonine formula is a formula given by Sonin for the integral of the product of three
*Bessel functions*. - The coefficients can be obtained from projecting the function " f ( x ) " onto the respective
*Bessel functions*: - If is the modified, or hyperbolic,
*Bessel function*of the first kind, we may define a function on the rationals by - The most familiar transcendental functions are the logarithm, the
*Bessel functions*are transcendental in general, but algebraic for some special parameter values. - For example, the solution for the time-dependent " start-up " process can be expressed in terms of
*Bessel functions*. - so all functions that are essentially special cases of it, such as
*Bessel functions*, can be expressed as limits of hypergeometric functions. - Dougall's own contributions to mathematics include works on
*Bessel functions*, Mathieu functions, hypergeometric series, and the Schl�fli double six.