MATLAB Function Reference |
Syntax
Description
Y = psi(X)
evaluates the function for each element of array X
. X
must be real and nonnegative. The function, also known as the digamma function, is the logarithmic derivative of the gamma function
Y = psi(k,X)
evaluates the k
th derivative of at the elements of X
. psi(0,X)
is the digamma function, psi(1,X)
is the trigamma function, psi(2,X)
is the tetragamma function, etc.
Y = psi(k0:k1,X)
evaluates derivatives of order k0
through k1
at X
. Y(k,j)
is the (k-1+k0)
th derivative of , evaluated at X(j)
.
Examples
Example 1. Use the psi
function to calculate Euler's constant, .
Example 2. The trigamma function of 2, psi(1,2)
, is the same as .
Example 3. This code produces the first page of Table 6.1 in Abramowitz and Stegun [1].
Example 4. This code produces a portion of Table 6.2 in [1].
See Also
References
[1] Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, 1965, Sections 6.3 and 6.4.
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