Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 ScorerGiZero

Source Notebook

Find zeros of the ScorerGi function

Contributed by: Jan Mangaldan

ResourceFunction["ScorerGiZero"][k]

represents the kth zero of the Scorer function Gi(x).

ResourceFunction["ScorerGiZero"][k,x0]

represents the kth zero less than x0.

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
N[ResourceFunction["ScorerGiZero"][k]] gives a numerical approximation so long as the specified zero exists.
ResourceFunction["ScorerGiZero"][k] represents the kth zero less than 0.
ResourceFunction["ScorerGiZero"] can be evaluated to arbitrary numerical precision.
ResourceFunction["ScorerGiZero"] automatically threads over lists.

Examples

Basic Examples (1) 

Evaluate numerically:

In[1]:=
N[ResourceFunction["ScorerGiZero"][1]]
Out[1]=

Scope (3) 

Evaluate to high precision:

In[2]:=
N[ResourceFunction["ScorerGiZero"][10], 50]
Out[2]=

Find the second zero of Gi(x) less than -500:

In[3]:=
N[ResourceFunction["ScorerGiZero"][2, -500]]
Out[3]=

ScorerGiZero threads elementwise over lists:

In[4]:=
ResourceFunction["ScorerGiZero"][{1, 2, 3}] // N
Out[4]=

Applications (1) 

Display zeros of the ScorerGi function over a subset of the reals:

In[5]:=
Plot[ScorerGi[z], {z, -20, 1}, Epilog -> {PointSize[0.03], Point[Table[{ResourceFunction["ScorerGiZero"][k], 0}, {k, 19}]]}]
Out[5]=

Version History

  • 1.0.0 – 07 January 2021

Source Metadata

  • Citation:
    • Gil A., Segura J., Temme N.M., On the zeros of the Scorer functions. Journal of Approximation Theory, vol. 120, no. 2, 253-266, 2003.
      DOI: 10.1016/S0021-9045(02)00022-9

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