Special Functions math library

Collection of Special Functions programs.

Description

A collection of special function programs valid in the entire complex plane. Includes Gamma, loggamma, psi, polygamma, error, zeta, and others.

Editor's Note: Please note that these files have the same names as files already included with MATLAB. Being aware of where they are on your path will help you determine when you're using these files and not the MathWorks versions.

Programs to calculate the complex Gamma, complex LogGamma, complex error, complex psi, complex Riemann zeta, vectorized factorial, vectorized double factorial functions as well as Bernoulli, Euler, Genocchi, and totient numbers.

• MATLAB release: MATLAB 6.0 (R12)

[asmail KAHDER]

very good

[asmail KAHDER]

very good

[Nikolai Tolich]

very useful

[teresa pulido]

very helpful. thanks! =)

[Laurie Mailhe]

Thanks, I found it very useful!

[Peter Theodossiou]

Very Useful.
Needs a similar routine for
polygamma.

[kadir tas]

 

[ETOR AMAFU]

i like your notes

[David Terr]

Looks great! I haven't even tried most of these yet, but I can tell it's a very useful package.

[Joerg Enderlein]

Very useful!

[Marinos Vouvakis]

 

[Amine Abdallah]

 

[Jaime Ramirez]

Really useful, includes functions that are not easy to find somewhere else

[Bart Selins]

This is exactly wat I needed, works perfect

[andrzej [e-mail]]

 

[Ben Petschel]

Nice work, these should be included in the core MATLAB.

Since erf rapidly goes to infinity along the i axis (e.g. erfz(1i*30) = 1i*Inf in floating point), it would be useful to have a function that calculates exp(z^2)*erf(z) or z*exp(z^2)*erfc(z).

[David Young]

Very helpful and useful (rating and comments based only on gamma and gammaln functions). Suggestions:

1. The code to allocate storage:

 f = 0.*z; % reserve space in advance

is not needed (indeed is wasteful), as preallocation is only useful ahead of a loop or to set up an array of a specific shape.

2. It might be worth switching to logical indexing rather than linear indexing - this would avoid the use of find() and the reshape at the end.

3. gammaln(z) returns infinities for abs(imag(z)) greater than about 226 and real(z) < 0. This is due to overflow of sin() in the reflection formula, but it is an unnecessary restriction as log(sin(z)) can be computed without overflow over a larger set of values than can sin(z). For example, we can use log(sin(x + iy)) (x and y real) is approximately equal to y + log(0.5i * exp(-1i * x)) for large positive y, and the approximation is good to machine accuracy if y > 18 or thereabouts. (For negative y the approximation is -y + log(-0.5i * exp(1i * x)).) Replacing log(sin()) by a call to a logsin() function that uses these approximations greatly extends the set of valid arguments.

[Bien]

Thanks! Needed a erfz function and this works well for me. This should be in the standard MATLAB function.

[Scott]

The package is generally excellent.
My only complaint is that the accuracy of the zeta function deterioriates rapidly for |z|>80.
For example, the script returns
0.541674252238781 - 0.348243845696725i
for the 29-th non-trivial zero, which is approximately 0.5+98.8311i.
 
If you ever have time for an upgrade it would be much appreciated!