Manuscript VIII-B@3 · VIII-B-v3.tex · section · 3aa6baa1

Lengths, one-sided laws, and areas

Reference specialization at mu0=pi/2 › Lengths, one-sided laws, and areas · lines 2579–2638

VIII-B@3#eq:reference-areas

At the reference point,

L_{α} = 2, W_{α} = \frac{3 65}{22} .

The full finite length table specializes to

For the last two constants,

χ 2 - b^{2} = \frac{15}{11} \frac{41}{25} = \frac{3 41}{11},

and

W_{α}^{2} = (- \frac{3}{22})^{2} + (\frac{15}{11})^{2} - \frac{9}{25} (\frac{15}{11})^{2} = \frac{585}{484} .

The persistent radial derivatives are $0$ and $- 5 /2$ . Born right slopes are $3/2$ , $341 /11$ , and $365 /22$ .

The areas are

Area (V_{i}) = {3/2, 3/2 - (15/22) s^{2}, s \leq 0, s > 0, Area (U_{i}^{\pm}) = \frac{9}{11} s^{2}, Area (Q_{i}) = \frac{7}{2} .

These follow from $r = 3$ , $β χ = 45/22$ , and $S_{α} = 1$ . The branch-boundary normal speed is

((2/3)^{2} + (1/15)^{2})^{- 1/2} = \frac{15}{101} .

Displayed formulas in this passage

VIII-B@3#eq:reference-areas · line 2621
$Area (V_{i}) = {3/2, 3/2 - (15/22) s^{2}, s \leq 0, s > 0, Area (U_{i}^{\pm}) = \frac{9}{11} s^{2}, Area (Q_{i}) = \frac{7}{2} .$
unlabeled · line 2582
$L_{α} = 2, W_{α} = \frac{3 65}{22} .$
unlabeled · line 2603
$χ 2 - b^{2} = \frac{15}{11} \frac{41}{25} = \frac{3 41}{11},$
unlabeled · line 2609
$W_{α}^{2} = (- \frac{3}{22})^{2} + (\frac{15}{11})^{2} - \frac{9}{25} (\frac{15}{11})^{2} = \frac{585}{484} .$
unlabeled · line 2634
$((2/3)^{2} + (1/15)^{2})^{- 1/2} = \frac{15}{101} .$