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NHoldFirst
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NHoldFirst

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is an attribute which specifies that the first argument to a function should not be affected by N.

Examples

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Basic Examples  (1)Summary of the most common use cases

Prevent N from affecting the first argument of a function:

In[1]:=1
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https://wolfram.com/xid/0i1rxhmbq-cpm2h
In[2]:=2
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https://wolfram.com/xid/0i1rxhmbq-k3vhc6
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1rxhmbq-fti8wk
Out[3]=3

Scope  (2)Survey of the scope of standard use cases

System symbols with the NHoldFirst attribute:

In[1]:=1
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https://wolfram.com/xid/0i1rxhmbq-l9p1c
Out[1]=1

The ^(th) zero of the zeta function on the critical line with the imaginary part greater than :

In[1]:=1
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https://wolfram.com/xid/0i1rxhmbq-jdf9md
Out[1]=1

N does not affect the index :

In[2]:=2
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https://wolfram.com/xid/0i1rxhmbq-w95c5
Out[2]=2

When the second argument is numeric, N evaluates numerically:

In[3]:=3
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https://wolfram.com/xid/0i1rxhmbq-l10tta
Out[3]=3

Applications  (1)Sample problems that can be solved with this function

Define an "inverse" for :

In[1]:=1
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https://wolfram.com/xid/0i1rxhmbq-idzc3k

Set the NHoldFirst attribute so that remains an integer:

In[2]:=2
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https://wolfram.com/xid/0i1rxhmbq-cm44jd

A symbolic representation of an inverse of :

In[3]:=3
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https://wolfram.com/xid/0i1rxhmbq-eyv8qp
Out[3]=3

This remains unmodified with N:

In[4]:=4
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https://wolfram.com/xid/0i1rxhmbq-g2qxu7
Out[4]=4

With a numeric value of x, the function binv evaluates numerically:

In[5]:=5
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https://wolfram.com/xid/0i1rxhmbq-ba5pum
Out[5]=5

Properties & Relations  (1)Properties of the function, and connections to other functions

HoldFirst prevents evaluation while NHoldFirst only prevents numerical evaluation:

In[1]:=1
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https://wolfram.com/xid/0i1rxhmbq-2rlzr
In[2]:=2
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https://wolfram.com/xid/0i1rxhmbq-dqg7
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1rxhmbq-cbp2j8
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0i1rxhmbq-m8utr
In[5]:=5
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https://wolfram.com/xid/0i1rxhmbq-cj9ifj
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0i1rxhmbq-dipegk
Out[6]=6

You can prevent both by setting both attributes:

In[7]:=7
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https://wolfram.com/xid/0i1rxhmbq-dvxl89
In[8]:=8
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https://wolfram.com/xid/0i1rxhmbq-csslcd
Out[8]=8
In[9]:=9
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https://wolfram.com/xid/0i1rxhmbq-y401c
Out[9]=9
Wolfram Research (1996), NHoldFirst, Wolfram Language function, https://reference.wolfram.com/language/ref/NHoldFirst.html.
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Wolfram Research (1996), NHoldFirst, Wolfram Language function, https://reference.wolfram.com/language/ref/NHoldFirst.html.

Text

Wolfram Research (1996), NHoldFirst, Wolfram Language function, https://reference.wolfram.com/language/ref/NHoldFirst.html.

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Wolfram Research (1996), NHoldFirst, Wolfram Language function, https://reference.wolfram.com/language/ref/NHoldFirst.html.

CMS

Wolfram Language. 1996. "NHoldFirst." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NHoldFirst.html.

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Wolfram Language. 1996. "NHoldFirst." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NHoldFirst.html.

APA

Wolfram Language. (1996). NHoldFirst. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NHoldFirst.html

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Wolfram Language. (1996). NHoldFirst. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NHoldFirst.html

BibTeX

@misc{reference.wolfram_2025_nholdfirst, author="Wolfram Research", title="{NHoldFirst}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/NHoldFirst.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_nholdfirst, author="Wolfram Research", title="{NHoldFirst}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/NHoldFirst.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_nholdfirst, organization={Wolfram Research}, title={NHoldFirst}, year={1996}, url={https://reference.wolfram.com/language/ref/NHoldFirst.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_nholdfirst, organization={Wolfram Research}, title={NHoldFirst}, year={1996}, url={https://reference.wolfram.com/language/ref/NHoldFirst.html}, note=[Accessed: 29-March-2025 ]}