Accurate bessel functions Jn(z), Yn(z), Hn(1)(z) and Hn(2)(z) of integer order and complex argument

1984 ◽  
Vol 35 ◽  
pp. C-559
Author(s):  
R.W.B. Ardill ◽  
K.J.M. Moriarty
Keyword(s):  
Bessel Functions ◽  
Integer Order ◽  
Complex Argument

scholarly journals Legendre polynomials in irrationality proofs

1980 ◽  
Vol 22 (3) ◽  
pp. 431-438 ◽  
Author(s):  
F. Beukers
Keyword(s):  
Legendre Polynomials ◽  
Bessel Functions ◽  
Integer Order ◽  
Zeros Of Bessel Functions

It is shown that a simple trick involving Legendre polynomials readily yields the irrationality of ea, , π2, and of the zeros of Bessel functions of integer order. Generalisation of this idea yields the irrationality of ζ(3).

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