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psi

Psi (polygamma) function

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Syntax

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

Description

Y = psi(X)evaluates theψfunction for each element of arrayX.Xmust be real and nonnegative. Theψfunction, also known as the digamma function, is the logarithmic derivative of the gamma function

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

Y = psi(k,X)evaluates thekth derivative ofψat the elements ofX.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 thepsifunction 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

References

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

Extended Capabilities

See Also

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Introduced before R2006a

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