The name is absent

The FT of function Yι_jn(r)∕rⁱ can be easily found using following equality

^-2π∕f.r _{= 4π}^(-₀∕₇∙(2π∕r)y_z,_m(∕)^_m(r),
l,m

which yields

Γ                 4π ʌ

J drY₂,_m(rWl_m^ = --Y₂,_m(f), (A.6)

writing down explicitly

1 - 3cos²0 4ττ ɔ , _zι .

--Я³-- ⁼ -y(l-3∞*4)∙

The derivative terms can also be calculated using FT

V²<Mr) = F’¹ [nv4(r)]] = -4π²<F^¹ [∕²⅛(f)].             (A.7)

For practical numerical calculation, FT is implemented via discrete Fourier transform
(DFT). That is, for an array of N uniformly sampled data h_n = h(t_n) (n = 0,1,2,..., N - 1),
if the sampling time-step is Δ, the frequency interval is ʌʃ = ɪ, i.e.,

I N                 N ∖   1

f’-' (-2..... ^l∙ "∙' ∙-∙T.V∆'              ^(A'⁸⁾

The FT of ∕ι(r) is approximately calculated as

ʃv-l              N-I

dth(t)e-^2π'^f"' ≈ Y₁ h_ke^^2πif"^tt A = Δ У h_ke-^2nikn/N,            (A.9)

fc=0                     k=0

the DFT is then defined as

N-I

h^Yh_ke-²”^ikn/N,                         (A. 10)

Ic=O

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