kummer {gaussratiovegind} | R Documentation |
Confluent D
-Hypergeometric Function
Description
Computes the Kummer's function, or confluent hypergeometric function.
Usage
kummer(a, b, z, eps = 1e-06)
Arguments
a |
numeric. |
b |
numeric |
z |
numeric vector. |
eps |
numeric. Precision for the sum (default 1e-06). |
Details
The Kummer's confluent hypergeometric function is given by:
\displaystyle{_1 F_1\left(a, b; z\right) = \sum_{n = 0}^{+\infty}{ \frac{ (a)_n }{ (b)_n } \frac{z^n}{n!} }}
where (z)_p
is the Pochhammer symbol (see pochhammer
).
The eps
argument gives the required precision for its computation.
It is the attr(, "epsilon")
attribute of the returned value.
Value
A numeric value: the value of the Kummer's function,
with two attributes attr(, "epsilon")
(precision of the result) and attr(, "k")
(number of iterations).
Author(s)
Pierre Santagostini, Angélina El Ghaziri, Nizar Bouhlel
References
El Ghaziri, A., Bouhlel, N., Sapoukhina, N., Rousseau, D., On the importance of non-Gaussianity in chlorophyll fluorescence imaging. Remote Sensing 15(2), 528 (2023). doi:10.3390/rs15020528