The Mathematical Analysis of Electrical And Optical Wave Motion On the Basis of
The Mathematical Analysis of Electrical And Optical Wave Motion On the Basis of
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It should be remem bered that ( 236 >- The corresponding integral in which K p (X) is replaced by J-p (Xf ) can also be evaluated in terms of Legendre functions, but the formulae are more complicated. The case p = m is discussed by Macdonald f.
It should be noticed that if we write cosh (a - ) = i cot i/r, cos (<) = coth a | /ooir\ sinh (a <) = i cosec \f/, sin (13 <) = i cosech * J "" three relations of type * See, for instance, the formulae given by H. M. Macdonald, Proc. London Math. Soc. Se...r. 2, Vol. 7, p. 147, and by the author, ibid. Vol. 12, Abstracts. T Loc. Cit. P. 142.
106 TOROIDAL COORDINATES [CH.
are satisfied and so the functions a, /3 can be used to obtain an electromagnetic field by the method of 5. It is easy to verify that the function u = (cosher- cos ^r)/ (a, ) ............ (239) satisfies the wave-equation, f being an arbitrary function.
We add here a few formulae for P n m (cosh cr), Q n m (cosh cr) ; these and other formulae will be found in the memoirs of Dr Hobson and Dr Barnes to which we have already referred.
What to read after The Mathematical Analysis of Electrical And Optical Wave Motion On the Basis of?
You can find similar books in the "Read Also" column, or choose other free books by Harry Bateman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
It should be remem bered that ( 236 >- The corresponding integral in which K p (X) is replaced by J-p (Xf ) can also be evaluated in terms of Legendre functions, but the formulae are more complicated. The case p = m is discussed by Macdonald f.
It should be noticed that if we write cosh (a - ) = i cot i/r, cos (<) = coth a | /ooir\ sinh (a <) = i cosec \f/, sin (13 <) = i cosech * J "" three relations of type * See, for instance, the formulae given by H. M. Macdonald, Proc. London Math. Soc. Se...r. 2, Vol. 7, p. 147, and by the author, ibid. Vol. 12, Abstracts. T Loc. Cit. P. 142.
106 TOROIDAL COORDINATES [CH.
are satisfied and so the functions a, /3 can be used to obtain an electromagnetic field by the method of 5. It is easy to verify that the function u = (cosher- cos ^r)/ (a, ) ............ (239) satisfies the wave-equation, f being an arbitrary function.
We add here a few formulae for P n m (cosh cr), Q n m (cosh cr) ; these and other formulae will be found in the memoirs of Dr Hobson and Dr Barnes to which we have already referred.
What to read after The Mathematical Analysis of Electrical And Optical Wave Motion On the Basis of?
You can find similar books in the "Read Also" column, or choose other free books by Harry Bateman to read onlineMoreLess
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