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gaussratiovegind (version 2.0.3)

kummer: Confluent \(D\)-Hypergeometric Function

Description

Computes the Kummer's function, or confluent hypergeometric function.

Usage

kummer(a, b, z, eps = 1e-06)

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).

Arguments

a

numeric.

b

numeric

z

numeric vector.

eps

numeric. Precision for the sum (default 1e-06).

Author

Pierre Santagostini, Angélina El Ghaziri, Nizar Bouhlel

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.

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). tools:::Rd_expr_doi("10.3390/rs15020528")