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NHoldFirst

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

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NHoldFirst

NHoldFirst

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)

Prevent N from affecting the first argument of a function:

Wolfram Language code: SetAttributes[f, NHoldFirst]
Wolfram Language code: N[f[3, Pi]]
Wolfram Language code: N[f[Pi, E], 20]

Scope  (2)

System symbols with the NHoldFirst attribute:

Wolfram Language code: ssymb = Cases[Map[ToExpression, Names["System`*"]], _Symbol]; Select[ssymb, MemberQ[Attributes[#], NHoldFirst]&]

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

Wolfram Language code: zz20 = ZetaZero[20, t + Pi]

N does not affect the index :

Wolfram Language code: N[zz20]

When the second argument is numeric, N evaluates numerically:

Wolfram Language code: N[zz20 /. t -> 1]

Applications  (1)

Define an "inverse" for :

Wolfram Language code: e : binv[k_Integer, x_ ? InexactNumberQ] := With[{r = Quiet[Check[z /. FindRoot[BesselJ[k, z] - x, {z, 0}, WorkingPrecision -> Precision[x]], $Failed]]}, r /; NumberQ[r]]

Set the NHoldFirst attribute so that remains an integer:

Wolfram Language code: SetAttributes[binv, NHoldFirst]

A symbolic representation of an inverse of :

Wolfram Language code: binv[1, x]

This remains unmodified with N:

Wolfram Language code: N[%]

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

Wolfram Language code: N[binv[1, 1 / Pi]]

Properties & Relations  (1)

HoldFirst prevents evaluation while NHoldFirst only prevents numerical evaluation:

Wolfram Language code: SetAttributes[f1, HoldFirst]
Wolfram Language code: f1[1 + 2, 3 + 4]
Wolfram Language code: N[%]
Wolfram Language code: SetAttributes[f2, NHoldFirst]
Wolfram Language code: f2[1 + 2, 3 + 4]
Wolfram Language code: N[%]

You can prevent both by setting both attributes:

Wolfram Language code: SetAttributes[f, {HoldFirst, NHoldFirst}]
Wolfram Language code: f[1 + 2, 3 + 4]
Wolfram Language code: N[%]
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.

CMS

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

BibTeX

@misc{reference.wolfram_2026_nholdfirst, author="Wolfram Research", title="{NHoldFirst}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/NHoldFirst.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_nholdfirst, organization={Wolfram Research}, title={NHoldFirst}, year={1996}, url={https://reference.wolfram.com/language/ref/NHoldFirst.html}, note=[Accessed: 12-June-2026]}