Table I
Identifications of coefficients.
ν even | ν odd |
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Term | Coefficients | Term | Coefficients |
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Y |
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| Z |
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V |
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| W |
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Y2 |
| ŝq1 | YZ |
| ŝq3 |
YV |
| ŝq2 | YW |
| ŝq4 |
V2 |
| ŝq5 | VZ |
| ŝq6 |
Z2 |
| ŝq8 | VW |
| ŝq7 |
ZW |
| ŝq9 | | | |
W2 |
| ŝq10 | | | |
Y3 |
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| Y2Z |
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Y2V |
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| Y2W |
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YV2 |
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| YVZ |
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YZ2 |
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| YVW |
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YZW |
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| V2Z |
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YW2 |
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| V2W |
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V3 |
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VZ2 |
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| z2W |
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VZW |
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| ZW2 |
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VW2 |
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| W3 |
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Table II
The
coefficients for an arbitrary plane symmetric surface.
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ŝx5 = 0 |
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ŝx9 = 0 | ŝx10 = 0 |
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Table III
The î coefficients.
îa = qcy | îc = cz |
îb = 1 | îd = 1 |
| ŝi3 = 2qθ32 |
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ŝi5 = 0 | ŝi6 = 0 |
| ŝi7 = 0 |
ŝi9 = 0 | |
ŝi10 = 0 | |
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Table IV
The
and
coefficients.
ρ1 = q′/2kα0α0′ ρ2 = kα0q′/2kα0′
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ŝσ5 = ρ2−ρ1α02 |
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ŝσ9 = ρ2cz | ŝτ9 = ρ3cz |
ŝσ10 = ŝσ6 | ŝτ10 = ŝτ5 |
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Table V
The
coefficients.
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| ŝτ8 = ŝϕ8 |
| ŝτ9 = ŝϕ9 |
| ŝτ10 = ŝ10 |
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Table VI
The
coefficients.
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ŝp5 = 0 | ŝp8 = ŝx8 |
ŝp9 = 0 | ŝp10 = 0 |
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Table VII
The second- and third-order ê coefficients.
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ŝeα = R0ŝiα+Î0yŝrα (α=8,9,10) |
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Table VIII
The second-order coefficients ωαβ.
β | ν even, A = a or c |
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α | 1 | 2 | 5 |
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1 | ya2 | yaυa | υa2 |
2 | 2yayb | yaυb+ybυa | 2υaυb |
5 | yb2 | ybυb | υb2 |
β | |
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α | 8 | 9 | 10 |
8 | zc2 | zcwc | wc2 |
9 | 2zczd | zcwd+zdwc | 2wcwd |
10 | zd2 | zdwd | wd2 |
β | ν odd, A = a or c |
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α | 3 | 4 | 6 | 7 |
3 | yazc | yawc | υazc | υawc |
4 | yazd | yawd | υazd | υawd |
6 | ybzc | ybwc | υbzc | υbwc |
7 | ybzd | ybwd | υbzd | υbwd |
Table IX
Third-order coefficients ωαβ.
β | ν even, A = a or c |
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α | 1 | 2 | 5 | 11 |
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1 | ya3 | ya2υa | yaυa2 | υa3 |
2 | 3ya2yb | ya(yaυb+2ybυa) | υa(2yaυb+ ybυa) | 3υa2υb |
5 | 3yayb2 | yb(2yaυb+ybυa) | υb(yaυb+ 2ybυa) | 3υabb2 |
11 | yb3 | yb2υb | ybυb2 | υb3 |
β | |
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α | 8 | 9 | 10 | 14 | 15 | 16 |
8 | yazc2 | yazcwc | yawc2 | υazc2 | υazcwc | υawc2 |
9 | 2yazczd | ya(zcwd+zdwc) | 2yawcwd | 2υazczd | υa(zcwd+zdwc) | 2υawcwd |
10 | yazd2 | yazdwd | yawd2 | υazd2 | υazdwd | υawd2 |
14 | ybzc2 | ybzcwc | ybwc2 | υbzc2 | υbzcwc | υbwc2 |
15 | 2ybzczd | yb(zcwd+zdwc) | 2ybwcwd | 2υbzczd | υb(zcwd+zdwc) | 2υbwcwd |
16 | ybzd2 | ybzdwd | ybwd2 | υbzd2 | υbzdwd | υbwd2 |
β | ν odd, A = b or d |
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α | 3 | 4 | 6 | 7 | 12 | 13 |
3 | ya2zc | ya2wc | yaυazc | yaυawc | υa2zc | υa2wc |
4 | ya2zd | ya2wd | yaυazd | yaυawd | υa2zd | υa2wd |
6 | 2yaybzc | 2yaybwc | (yaυb+ybυa)zc | (yaυb+ybυa)wc | 2υaυbzc | 2υaυbwc |
7 | 2yaybzd | 2yaybwd | (yaυb+ybυa)zd | (yaυb+ybυa)wd | 2υaυbzd | 2υaυbwd |
12 | yb2zc | yb2wc | ybυbzc | ybυbwc | υb2zc | υb2wc |
13 | yb2zd | yb2wd | ybυbzd | ybυbwd | υb2zd | υb2wd |
β | |
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α | 17 | 18 | 19 | 20 |
17 | zc3 | wczc2 | zcwc2 | wc3 |
18 | 3zc2zd | zc(zcwd+2wczd) | wc(2zcwd+wczd) | 3wc2wd |
19 | 3zczd2 | zd(2zcwd+zdwc) | wd(zcwd+2wczd) | 3wcwd2 |
20 | zd3 | zd2wd | zdwd2 | wd3 |
Table X
Third-order iteration equations. The subscript A has been omitted from all tα,
, and
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A=a or b, ν even |
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A=c or d, ν odd |
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Table XI
The
coefficients for spherical surfaces.
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ŝx5 = 0 |
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ŝx9 = 0 | ŝx10 = 0 |
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Table XII
The
and
coefficients for spherical surfaces.
ρ1 = q′/2kα0α0′ ρ2 = kα0q′/2α0′
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ŝσ1=cρ1ŝz1 |
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| ŝτ2=ρ3ŝσ2 |
ŝσ5=n0x(ρ2−α02ρ1) |
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ŝσ8=cρ1ŝx8 |
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ŝσ9 = cρ2 | ŝτ9=ρ3ŝσ9 |
ŝσ10=ŝσ5 | ŝτ10=ŝr5 |
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