relations%20to%20other%20functions

(0.009 seconds)

21—21 of 21 matching pages

… ►A similar relation holds for the changes in sign of the coefficients of

f(-z)

, and hence for the number of negative zeros of

f(z)

. … ►Addition of

-\frac{1}{3}a

to each of these roots gives the roots of

f(z)=0

. … ►Add

-\tfrac{1}{4}a

to the roots of

g(w)=0

to get those of

f(z)=0

. … ►Resolvent cubic is

z^{3}+12z^{2}+20z+9=0

with roots

\theta_{1}=-1

\theta_{2}=-\tfrac{1}{2}(11+\sqrt{85})

\theta_{3}=-\tfrac{1}{2}(11-\sqrt{85})

, and

\sqrt{-\theta_{1}}=1

\sqrt{-\theta_{2}}=\tfrac{1}{2}(\sqrt{17}+\sqrt{5})

\sqrt{-\theta_{3}}=\tfrac{1}{2}(\sqrt{17}-\sqrt{5})

. … ►

…