why changing the order of `Format` causes error?

Question

I am trying the solution given in is-it-possible-to-change-customize-some-conversions-done-by-texform which works very well except changing the order of the Format command causes an error on some symbols.

I do not know if this is Mathematica own issue with the command Format or if it is related to the package I am using.

First I installed the nice package MathematicaTeXUtilities using the command

 Get["https://raw.githubusercontent.com/jkuczm/MathematicaTeXUtilities/master/BootstrapInstall.m"]

Here is MWE. Using the following order, with fresh kernel, show no error

Needs["TeXUtilities`"]
Unprotect[Hypergeometric1F1,HypergeometricU];
Format[ Hypergeometric1F1, TeXForm] = TeXVerbatim@"\\operatorname{Hypergeometric1F1}";
Format[ HypergeometricU, TeXForm] = TeXVerbatim@"\\operatorname{HypergeometricU}";
Protect[Hypergeometric1F1,HypergeometricU];

Now, changed the order of Format command, and using fresh kernel (must restart the kernel to see the error), an error message shows up

Needs["TeXUtilities`"]
Unprotect[Hypergeometric1F1,HypergeometricU];
Format[ HypergeometricU, TeXForm] = TeXVerbatim@"\\operatorname{HypergeometricU}";
Format[ Hypergeometric1F1, TeXForm] = TeXVerbatim@"\\operatorname{Hypergeometric1F1}";
Protect[Hypergeometric1F1,HypergeometricU];

I thought at first that the order of symbols in Protect has to match the order of Format commands. But this does not make sense. And I found by trial and error a case where the errors show up even when the order or Protect match order of Format. Here it is (fresh kernel)

Needs["TeXUtilities`"]
Unprotect[HypergeometricU,LaguerreL,HermiteH,Hypergeometric1F1,Erf,Erfc];
Format[ HypergeometricU, TeXForm] = TeXVerbatim@"\\operatorname{HypergeometricU}"
Format[ LaguerreL, TeXForm] = TeXVerbatim@"\\operatorname{LaguerreL}"
Format[ HermiteH, TeXForm] = TeXVerbatim@"\\operatorname{HermiteH}"
Format[ Hypergeometric1F1, TeXForm] = TeXVerbatim@"\\operatorname{Hypergeometric1F1}"
Format[ Erfc, TeXForm] = TeXVerbatim@"\\operatorname{Erfc}"
Format[ Erf, TeXForm] = TeXVerbatim@"\\operatorname{Erf}"
Protect[HypergeometricU,LaguerreL,HermiteH,Hypergeometric1F1,Erf,Erfc];

So I am not sure what is going on now. Any ideas?

As a workaround, now I Format them one by one, instead of the batch mode and error went away

Needs["TeXUtilities`"]

Unprotect[Hypergeometric1F1];
Format[ Hypergeometric1F1, TeXForm] = TeXVerbatim@"\\operatorname{Hypergeometric1F1}";
Protect[Hypergeometric1F1];

Unprotect[HypergeometricU];
Format[ HypergeometricU, TeXForm] = TeXVerbatim@"\\operatorname{HypergeometricU}";
Protect[HypergeometricU];

Answer 1

Many System` symbols autoload when they are used. This is what is happening in your example. For instance, from a fresh kernel:

OwnValues @ HypergeometricU

{HoldPattern[HypergeometricU] :> System`Dump`AutoLoad[Hold[HypergeometricU], Hold[HypergeometricPFQ, HypergeometricPFQRegularized, HypergeometricU], "SpecialFunctions`HypergeometricPFQ`"] /; System`Dump`TestLoad}

This means that when HypergeometricU is evaluated, System`Dump`AutoLoad is called. Note the second argument, namely Hold[HypergeometricPFQ, HypergeometricPFQRegularized, HypergeometricU]. These symbols get protected during autoloading. So, this is what is happening during your example:

Unprotect[HypergeometricU,LaguerreL,HermiteH,Hypergeometric1F1,Erf,Erfc];

HypergeometricU gets unprotected

Format[ HypergeometricU, TeXForm] = TeXVerbatim@"\\operatorname{HypergeometricU}"

First, HypergeometricU is evaluated (Format has no Hold* attributes). Then, the TeXForm Format is stored. Since HypergeometricU is evaluated, it autoloads, and during this process, HypergeometricPFQ, HypergeometricPFQRegularized, HypergeometricU all get protected.

Format[ Hypergeometric1F1, TeXForm] = TeXVerbatim@"\\operatorname{Hypergeometric1F1}"

Since Hypergeometric1F1 is now Protected, you get a Message, and no Format is stored.