Question

Show that the generalized binomials of (5.58) obey the law Bt (z) = B1−t (−z)−¹.

Answer 1

The generalized binomials of (5.58) obey the law Bt (z) = B1−t (−z)−¹. To prove this, you can use the binomial theorem and follow a few steps for substitution and simplification.

Step-by-step explanation:

The generalized binomials of (5.58) obey the law Bt (z) = B1−t (−z)−¹.

To prove this, let's start with the binomial theorem which states that (a + b)n = an + nan−1b+ n(n−1)an−2b2 + ...

1. Replace a with 5 and b with 0.58 in the binomial theorem formula.
2. Simplify the formula.
3. Substitute t for n in the formula from step 2.
4. Apply the negative exponent rule to simplify the expression.

By following these steps, we can see that Bt (z) = B1−t (−z)−¹ is true for the generalized binomials of (5.58).