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MTM[zeta] - the Riemann Zeta function
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Calling Sequence
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zeta(z)
zeta(n,z)
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Parameters
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z
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algebraic expression
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n
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(optional) algebraic expression, understood to be a non-negative integer
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Description
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The zeta function is defined for Re(z)>1 by
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and is extended to the rest of the complex plane (except for the point z=1) by analytic continuation. The point z=1 is a simple pole.
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The call zeta(n, z) gives the nth derivative of the zeta function,
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![Zeta(n, z) = Diff(Zeta(z), [`$`(z, n)])](/support/helpjp/helpview.aspx?si=7703/file04893/math63.png)
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zeta(z) will evaluate by default only when the result is an exact value, or when the input z is a floating point number. When z is a symbolic expression, it will remain in function form so that it can be manipulated symbolically by itself or as part of a larger expression.
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If z is an array or matrix, the result is an element-wise mapping over z.
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