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References

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  1. A. Cohen, C. Acquista, J. A. Cooney, Appl. Opt. 19, 2264 (1980).
    [CrossRef] [PubMed]
  2. T. B. A. Senior, R. F. Goodrich, Proc. IEE London 111, 907 (1964).
  3. R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966), p. 84 et seq.

1980

1964

T. B. A. Senior, R. F. Goodrich, Proc. IEE London 111, 907 (1964).

Acquista, C.

Cohen, A.

Cooney, J. A.

Goodrich, R. F.

T. B. A. Senior, R. F. Goodrich, Proc. IEE London 111, 907 (1964).

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966), p. 84 et seq.

Senior, T. B. A.

T. B. A. Senior, R. F. Goodrich, Proc. IEE London 111, 907 (1964).

Appl. Opt.

Proc. IEE London

T. B. A. Senior, R. F. Goodrich, Proc. IEE London 111, 907 (1964).

Other

R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966), p. 84 et seq.

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Equations (14)

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Q ext = ( 4 / x 2 ) Re S ,
S = n = 1 ( n + ½ ) ( a n + b n ) .
a n = ψ n ( x ) / ξ n ( 1 ) ( x ) ,             b n = ψ n ( x ) / ξ n ( 1 ) ( x ) ,
ψ n ( x ) = x j n ( x ) ,             ξ n ( 1 ) ( x ) = x h n ( 1 ) ( x ) ,
S = C [ ψ ν - 1 / 2 ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) + ψ ν - 1 / 2 ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) ] ν d ν 1 + exp ( 2 π i ν ) - ½ ,
S = S 0 + S c ( 1 ) + S c ( 2 ) ,
S 0 = 0 x ν d ν - ½ + - i 0 exp ( - 2 π i ν ) 1 + exp ( - 2 π i ν ) ν d ν - 0 + i exp ( 2 π i ν ) 1 + exp ( 2 π i ν ) ν d ν ,
S c ( 1 ) = - 1 2 - + i + i [ ξ ν - 1 / 2 ( 2 ) ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) + ξ ν - 1 / 2 ( 2 ) ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) ] exp ( 2 π i ν ) 1 + exp ( 2 π i ν ) ν d ν ,
S c ( 2 ) = 1 2 - x [ ξ ν - 1 / 2 ( 2 ) ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) + ξ ν - 1 / 2 ( 2 ) ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) ] ν d ν + x [ ψ ν - 1 / 2 ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) + ψ ν - 1 / 2 ( x ) ξ ν - 1 / 2 ( 1 ) ( x ) ] ν d ν .
S 0 = 1 2 ( x 2 - 11 12 ) .
S c ( 2 ) = x 4 / 3 ( 0.082972 + i 0.144019 ) + O ( x 2 / 3 ) .
lim x Q ext = 2.
a n = α n ψ n ( x ) - ψ n ( x ) α n ξ n ( 1 ) ( x ) - ξ n ( 1 ) ( x ) , b n = β n ψ n ( x ) - ψ n ( x ) β n ξ n ( 1 ) ( x ) - ξ n ( 1 ) ( x ) ,
α n = m 2 β n = m ψ n ( m x ) ψ n ( m x ) ,

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