<p>Function N.γ(r;ρ)</p>

2dcffd84-f20e-4283-896d-a9d56779d34c 5 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

r ρ N.γ α ρ tan 1 ρ tan 2^+ sqrt + atan eval : N α tan 2^eval : K.p 2 N * N 1 + / e π 2 / ρ + (ρ tan *^* eval : X.0 21 r - (* ρ tan * eval : i 14 range X i el X.0 : ψ X.0 ρ tan - atan eval : c.mod ρ tan 1 ψ tan ρ tan * + (K.p * e 2 ψ * ρ tan *^* 1 - Max eval : X.c 1 r - 1 r - (2^0 c.mod 0 ≡ 1 r - c.mod / cases + sqrt + (ρ tan * eval : X.0 X.c - abs 0.001 > X.0 X.c : break if 51 line for 2 c.mod * X.c * ρ tan + 1 ψ tan 2^+ / eval r 01 lele cases ρ 0 atan 1 atan lele cases 61 line :

I have modfied c to get rid of the complex results discussed earlier. The modification to c seems to produce fairly correct results within the domain of this function.

Matrix ∠ 0455 range (° * : r 0 0.2 0.4 0.5 0.6 0.7 0.8 0.9 0.95 1110 mat : 21 sys i 1 ∠ rows range j 1 r cols range M i j el r j el ∠ i el N.γ : for for ∠ ° / M augment 31 line :

Matrix 000000000005 0.25 0.22 0.2 0.18 0.17 0.15 0.14 0.12 0.11 0.09 10 0.84 0.72 0.59 0.53 0.47 0.4 0.34 0.28 0.24 0.17 15 2.06 1.67 1.29 1.11 0.93 0.77 0.62 0.46 0.38 0.25 20 4.5 3.48 2.51 2.06 1.65 1.29 0.96 0.67 0.53 0.32 25 9.54 7.04 4.67 3.64 2.75 2 1.39 0.9 0.68 0.38 30 20.61 14.42 8.68 6.33 4.43 2.97 1.9 1.12 0.81 0.43 35 47.15 31.17 16.63 11.12 7.05 4.25 2.45 1.32 0.92 0.47 40 118.86 73.72 33.87 20.19 11.19 5.88 3.01 1.5 0.99 0.49 45 346.07 200.39 76.44 38.9 17.9 7.83 3.62 1.66 1.03 0.5 1011 mat

r 0 0.2 0.4 0.5 0.6 0.7 0.8 0.9 0.95 1110 mat :

Metric Y\X r augment (: Y\X 0 0.2 0.4 0.5 0.6 0.7 0.8 0.9 0.95 1111 mat

bilinearMatrix Metric Matrix stack :

bilinearMatrix Y\X 0 0.2 0.4 0.5 0.6 0.7 0.8 0.9 0.95 1000000000005 0.25 0.22 0.2 0.18 0.17 0.15 0.14 0.12 0.11 0.09 10 0.84 0.72 0.59 0.53 0.47 0.4 0.34 0.28 0.24 0.17 15 2.06 1.67 1.29 1.11 0.93 0.77 0.62 0.46 0.38 0.25 20 4.5 3.48 2.51 2.06 1.65 1.29 0.96 0.67 0.53 0.32 25 9.54 7.04 4.67 3.64 2.75 2 1.39 0.9 0.68 0.38 30 20.61 14.42 8.68 6.33 4.43 2.97 1.9 1.12 0.81 0.43 35 47.15 31.17 16.63 11.12 7.05 4.25 2.45 1.32 0.92 0.47 40 118.86 73.72 33.87 20.19 11.19 5.88 3.01 1.5 0.99 0.49 45 346.07 200.39 76.44 38.9 17.9 7.83 3.62 1.66 1.03 0.5 1111 mat

M bilinearMatrix :

bilinear is univrsal to all CAS [Computer Algebra System]
in 'Matrix' ... ∠ is converted in [°] x y M bilinear A M 11 range 2 M cols range el : B M 2 M rows range 11 range el : C M 2 M rows range 2 M cols range el : j 1 A length 2 range D j el B C 1 C rows range j j range el y linterp : for A transpose D x linterp 51 line :

sanity check bilinear 0.45 25 M bilinear 4.16

... r ...

° ∠

ruhet 0.45 :

ruhet 25 ° * N.γ 4.14

sanity check bilinear 0.7 45 M bilinear 7.83