03-20-2020, 12:41 PM

Generating The Binomial Series

The binomial series (1 + b*x)^a can be generated by the series:

(1 + b*x)^a = 1 + a*b*x + a*(a-1) / 2! * (b*x)^2 + a*(a-1)*(a-2) / 3! * (b*x)^3 + ....

= ∑ ( a NCR k) * (b * x)^k for k = 0 from ∞

where:

(a NCR k) = (a * (a - 1) * (a - 2) * ... * (a - k + 1) ) / k!

The values a and b can be complex and do not have to be integers.

If a is not a positive integer, the series continues on indefinitely.

Output: List 5 has the coefficients. The program BINOMSRS calculates the coefficients and any approximation of that series (f(x)).

The program listing and download can be found: http://edspi31415.blogspot.com/2020/03/c...omial.html

The binomial series (1 + b*x)^a can be generated by the series:

(1 + b*x)^a = 1 + a*b*x + a*(a-1) / 2! * (b*x)^2 + a*(a-1)*(a-2) / 3! * (b*x)^3 + ....

= ∑ ( a NCR k) * (b * x)^k for k = 0 from ∞

where:

(a NCR k) = (a * (a - 1) * (a - 2) * ... * (a - k + 1) ) / k!

The values a and b can be complex and do not have to be integers.

If a is not a positive integer, the series continues on indefinitely.

Output: List 5 has the coefficients. The program BINOMSRS calculates the coefficients and any approximation of that series (f(x)).

The program listing and download can be found: http://edspi31415.blogspot.com/2020/03/c...omial.html