| 31. | There is a useful identity involving Bessel functions called the Jacobi-Anger expansion which can be used to derive
|
| 32. | Where " I " k ( z ) is the modified Bessel function of the first kind.
|
| 33. | His solution takes the form of an expansion of modified ( hyperbolic ) Bessel functions of the first kind.
|
| 34. | The next simplest cases of a disc or square involve, respectively, Bessel functions and Jacobi theta functions.
|
| 35. | Where " I " 0 is the zero-th order modified Bessel function of the first kind.
|
| 36. | Hopf s collaboration with Sommerfeld on integral representations of Bessel Functions resulted in the publication of a paper in 1911.
|
| 37. | Macdonald worked on electric waves and solved difficult problems regarding diffraction of these waves by summing series of Bessel functions.
|
| 38. | Determination of the wave number is therefore possible by determining the roots of the Bessel function of the first kind.
|
| 39. | Lattice light sheet microscopy aims at reducing the intensity of the outer lobes of the Bessel functions by destructive interference.
|
| 40. | Where M is a confluent hypergeometric function and \ mathcal J _ 0 is a Bessel function of the first kind.
|
