Dr. John Kolassa
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obtained by extracting coefficients from the expansion, is as follows | obtained by extracting coefficients from the expansion, is as follows | ||
:<math forward>\begin{array}{lcr} | :<math forward>\begin{array}{lcr} | ||
| − | \kappa_1 &=& \mu_1 | + | \kappa_1 &=& \mu_1 \\ |
| − | \kappa_2 &=& \mu_2 - \mu_1^2 | + | \kappa_2 &=& \mu_2 - \mu_1^2\\ |
\kappa_3 &=& \mu_3 - 3\mu_2\mu_1 + 2\mu_1^3\\ | \kappa_3 &=& \mu_3 - 3\mu_2\mu_1 + 2\mu_1^3\\ | ||
| − | \kappa_4 &=& \mu_4 - 4\mu_3\mu_1 - 3\mu_2^2 + 12\mu_2\mu_1^2 -6\mu_1^4. | + | \kappa_4 &=& \mu_4 - 4\mu_3\mu_1 - 3\mu_2^2 + 12\mu_2\mu_1^2 -6\mu_1^4. |
</math> | </math> | ||
In the reverse direction | In the reverse direction | ||
:<math reverse>\begin{array}{lcr} | :<math reverse>\begin{array}{lcr} | ||
| − | \mu_2 &=& \kappa_2 + \kappa_1^2 | + | \mu_2 &=& \kappa_2 + \kappa_1^2\\ |
\mu_3 &=& \kappa_3 + 3\kappa_2\kappa_1 + \kappa_1^3\\ | \mu_3 &=& \kappa_3 + 3\kappa_2\kappa_1 + \kappa_1^3\\ | ||
| − | \mu_4 &=& \kappa_4 + 4\kappa_3\kappa_1 + 3\kappa_2^2 + 6\kappa_2\kappa_1^2 + \kappa_1^4. | + | \mu_4 &=& \kappa_4 + 4\kappa_3\kappa_1 + 3\kappa_2^2 + 6\kappa_2\kappa_1^2 + \kappa_1^4. |
</math> | </math> | ||
In particular, | In particular, | ||
