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  1. E. Lommel, Abhandl. Bayer. Akad. 15, 529 (1886).
  2. E. Lommel, Abhandl. Bayer. Akad. 15, 229 (1884).
  3. B. R. A. Nijboer, “The diffraction theory of aberrations” doctoral thesis, Groningen, 1942.
  4. E. H. Linfoot, Recent Advances in Optics (Oxford University Press, Oxford, 1955), p. 54.
  5. G. N. Watson, A Treatise on Bessel Functions (Cambridge University Press, Cambridge, 1948), p. 368.
  6. F. Oberhettinger, Tabellen zur Fourier Transformation (Springer-Verlag, Berlin, 1957), p. 57.

1886 (1)

E. Lommel, Abhandl. Bayer. Akad. 15, 529 (1886).

1884 (1)

E. Lommel, Abhandl. Bayer. Akad. 15, 229 (1884).

Linfoot, E. H.

E. H. Linfoot, Recent Advances in Optics (Oxford University Press, Oxford, 1955), p. 54.

Lommel, E.

E. Lommel, Abhandl. Bayer. Akad. 15, 529 (1886).

E. Lommel, Abhandl. Bayer. Akad. 15, 229 (1884).

Nijboer, B. R. A.

B. R. A. Nijboer, “The diffraction theory of aberrations” doctoral thesis, Groningen, 1942.

Oberhettinger, F.

F. Oberhettinger, Tabellen zur Fourier Transformation (Springer-Verlag, Berlin, 1957), p. 57.

Watson, G. N.

G. N. Watson, A Treatise on Bessel Functions (Cambridge University Press, Cambridge, 1948), p. 368.

Abhandl. Bayer. Akad. (2)

E. Lommel, Abhandl. Bayer. Akad. 15, 529 (1886).

E. Lommel, Abhandl. Bayer. Akad. 15, 229 (1884).

Other (4)

B. R. A. Nijboer, “The diffraction theory of aberrations” doctoral thesis, Groningen, 1942.

E. H. Linfoot, Recent Advances in Optics (Oxford University Press, Oxford, 1955), p. 54.

G. N. Watson, A Treatise on Bessel Functions (Cambridge University Press, Cambridge, 1948), p. 368.

F. Oberhettinger, Tabellen zur Fourier Transformation (Springer-Verlag, Berlin, 1957), p. 57.

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Equations (6)

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a ( υ ) = 1 2 1 e ipx e i υ x 2 d x ,
e i z cos θ = ( π 2 z ) 1 2 n = 0 ( 2 n + 1 ) i n J n + 1 2 ( z ) P n ( cos θ ) ,
e i p x 2 = e ( i / 2 ) p e ( i / 2 ) p ( 2 x 2 1 ) = ( π p ) 1 2 e ( i p / 2 ) n = 0 ( 2 n + 1 ) i n J n + 1 2 ( p 2 ) P n ( 2 x 2 1 ) .
1 1 P n ( 2 x 2 1 ) e i υ z d x = 2 0 1 P n ( 2 x 2 1 ) cos υ xdx = π J n + 1 2 ( υ / 2 ) J n 1 2 ( υ / 2 ) .
a ( υ ) = π 2 ( π p ) 1 2 e ( i p / 2 ) n = 0 i n ( 2 n + 1 ) J n + 1 2 ( p 2 ) J n + 1 2 ( υ 2 ) J n 1 2 ( υ 2 ) ,
a ( υ ) = ( 2 υ ) ( π p ) 1 2 e ( i p / 2 ) n = 0 ( i ) n ( 2 n + 1 ) J n + 1 2 ( p 2 ) J 2 n + 1 ( υ ) .