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psi

Psi (polygamma) function

Syntax

Y = psi(X)
Y = psi(k,X)

Description

Y = psi(X) evaluates the ψ function for each element of array X. X must be real and nonnegative. The ψ function, also known as the digamma function, is the logarithmic derivative of the gamma function

ψ(x)=digamma(x)=d(log(Γ(x)))dx=d(Γ(x))/dxΓ(x)

Y = psi(k,X) evaluates the kth derivative of ψ 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.

Examples

Example 1

Use the psi function to calculate Euler's constant, γ.

format long
-psi(1)
ans =
   0.57721566490153

-psi(0,1)
ans =
   0.57721566490153

Example 2

The trigamma function of 2, psi(1,2), is the same as (π2/6) – 1.

format long
psi(1,2)
ans =
   0.64493406684823

pi^2/6 - 1
ans =
   0.64493406684823

More About

collapse all

Tall Array Support

This function supports tall arrays with the limitation:

For the syntax Y = psi(k,X), k must be a non-tall scalar.

For more information, see Tall Arrays.

References

[1] Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, 1965, Sections 6.3 and 6.4.

See Also

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Introduced before R2006a

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