Confluent hypergeometric function

Solves Kummer's differential equation.

Description

This function estimates the solution to Kummer's differential equation within a specified tolerance. Kummer's differential equation is given by:

    x*g''(x) + (b - x)*g'(x) - a*g(x) = 0

The code executes a while loop to calculate the generalized hypergeometric series within a specified tolerance.

Supports inputs of x in the form of a scalar, row vector, or column vector.

• MATLAB release: MATLAB 7.10 (2010a)

[Frederic]

 

[Frederic]

Works very well and is very fast. One quick suggestion for those wanting vector 'x' arguments:
[...]
ar = [1 a a+[1:N-1]]; br = [1 b b+[1:N-1]];
fact = cumprod(ar)./cumprod(br)./factorial([0:N]);
for i = 1:length(x)
f(i) = fact*[x(i).^[0:N]]';
end

[Patrick]

Hello Frederic,
Your suggestion to handle vector inputs is a good one. However, I am trying to avoid for loops to realize the speed. I was trying to include the ability to handle vector inputs in the original submission but couldn't figure out how to do it at the time.

I just submitted an update to the code that handles column vector inputs for x and avoids for loops. I'm not sure how long it takes for the review process, but keep an eye out for it if you're interested.

[Frederic]

Awesome; thanks a lot -- my suggestion was naive.
I haven't tried yet but I peeked at the updated code and I'll give it a shot later on.

[Michael Todd]

Very nice, thank you.