zeta - Compute the Riemann zeta function

Syntax

Y = zeta(X) Y = zeta(n, X)

Y = zeta(X) evaluates the zeta function at the elements of X, a numeric matrix, or a symbolic matrix. The zeta function is defined by

Y = zeta(n, X) returns the n-th derivative of zeta(X).

Compute the Riemann zeta function for the number:

zeta(1.5)

The result is:

ans =
    2.6124

Compute the Riemann zeta function for the matrix:

zeta(1.2:0.1:2.1)

The result is:

ans =
Columns 1 through 6

  5.5916    3.9319    3.1055    2.6124    2.2858    2.0543

Columns 7 through 10

  1.8822    1.7497    1.6449    1.5602

Compute the Riemann zeta function for the matrix of the symbolic expressions:

syms x y;
zeta([x 2; 4 x + y])

The result is:

ans =
[ zeta(x),      pi^2/6]
[ pi^4/90, zeta(x + y)]

Differentiate the Riemann zeta function:

diff(zeta(x), x, 3)

The result is:

ans =
zeta(x, 3)

vpa (sym)

ztrans (sym)

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