Mixing
Stop the Zeta function from evaluating
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I have a function F whose power series i want to find using Series.
It gives me the result I want, except there is a term of $pi^4/10800$, and i want it to tell me if the result is Zeta[2]^2/300 or Zeta[4]/120. Is there a way to force the Zeta function to not evaluate?
F[x] = Integrate[Binomial[x, k], k, 0, x];
Series[F[x], x, 0, 3] // TeXForm
$x+fracpi ^2 x^336+Oleft(x^4right)$
I want the output to be $x+x^3fraczeta(2)6$ instead.
calculus-and-analysis evaluation
edited Sep 3 at 20:35
Carl Woll
56.1k272146
asked Sep 3 at 20:17
Michael Klyachman
586
add a comment |Â
up vote
11
down vote
favorite
I have a function F whose power series i want to find using Series.
It gives me the result I want, except there is a term of $pi^4/10800$, and i want it to tell me if the result is Zeta[2]^2/300 or Zeta[4]/120. Is there a way to force the Zeta function to not evaluate?
F[x] = Integrate[Binomial[x, k], k, 0, x];
Series[F[x], x, 0, 3] // TeXForm
$x+fracpi ^2 x^336+Oleft(x^4right)$
I want the output to be $x+x^3fraczeta(2)6$ instead.
calculus-and-analysis evaluation
edited Sep 3 at 20:35
Carl Woll
56.1k272146
asked Sep 3 at 20:17
Michael Klyachman
586
add a comment |Â
up vote
11
down vote
favorite
up vote
11
down vote
favorite
I have a function F whose power series i want to find using Series.
It gives me the result I want, except there is a term of $pi^4/10800$, and i want it to tell me if the result is Zeta[2]^2/300 or Zeta[4]/120. Is there a way to force the Zeta function to not evaluate?
F[x] = Integrate[Binomial[x, k], k, 0, x];
Series[F[x], x, 0, 3] // TeXForm
$x+fracpi ^2 x^336+Oleft(x^4right)$
I want the output to be $x+x^3fraczeta(2)6$ instead.
calculus-and-analysis evaluation
edited Sep 3 at 20:35
Carl Woll
56.1k272146
asked Sep 3 at 20:17
Michael Klyachman
586
I have a function F whose power series i want to find using Series.
It gives me the result I want, except there is a term of $pi^4/10800$, and i want it to tell me if the result is Zeta[2]^2/300 or Zeta[4]/120. Is there a way to force the Zeta function to not evaluate?
F[x] = Integrate[Binomial[x, k], k, 0, x];
Series[F[x], x, 0, 3] // TeXForm
$x+fracpi ^2 x^336+Oleft(x^4right)$
I want the output to be $x+x^3fraczeta(2)6$ instead.
calculus-and-analysis evaluation
edited Sep 3 at 20:35
Carl Woll
56.1k272146
asked Sep 3 at 20:17
Michael Klyachman
586
edited Sep 3 at 20:35
Carl Woll
56.1k272146
edited Sep 3 at 20:35
Carl Woll
56.1k272146
edited Sep 3 at 20:35
Carl Woll
56.1k272146
56.1k272146
asked Sep 3 at 20:17
Michael Klyachman
586
asked Sep 3 at 20:17
Michael Klyachman
586
asked Sep 3 at 20:17
Michael Klyachman
586
586
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
15
down vote
accepted
You could Block Zeta so that it doesn't evaluate:
Block[Zeta=Inactive[Zeta],
Series[F[x],x,0,6]
] //TeXForm
$x+frac16 x^3 operatornameZeta(2,1)-frac16 x^4 operatornameZeta(3)+frac160 x^5
left(operatornameZeta(2,1)^2+9 operatornameZeta(4,1)right)+x^6 left(-frac130 operatornameZeta(3)
operatornameZeta(2,1)-frac2 operatornameZeta(5)15right)+Oleft(x^7right)$
answered Sep 3 at 20:28
Carl Woll
56.1k272146
You could postprocess the result withres /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].
– Chip Hurst
Sep 3 at 20:52
Also it's strangeInactive[Zeta]doesn't format in TraditionalForm withζ.
– Chip Hurst
Sep 3 at 20:53
@ChipHurst What aboutres1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s]? And if you want to activate it,res1 /.[Zeta][s_] :> Zeta[s]
– theorist
Sep 4 at 0:41
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
15
down vote
accepted
You could Block Zeta so that it doesn't evaluate:
Block[Zeta=Inactive[Zeta],
Series[F[x],x,0,6]
] //TeXForm
$x+frac16 x^3 operatornameZeta(2,1)-frac16 x^4 operatornameZeta(3)+frac160 x^5
left(operatornameZeta(2,1)^2+9 operatornameZeta(4,1)right)+x^6 left(-frac130 operatornameZeta(3)
operatornameZeta(2,1)-frac2 operatornameZeta(5)15right)+Oleft(x^7right)$
answered Sep 3 at 20:28
Carl Woll
56.1k272146
You could postprocess the result withres /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].
– Chip Hurst
Sep 3 at 20:52
Also it's strangeInactive[Zeta]doesn't format in TraditionalForm withζ.
– Chip Hurst
Sep 3 at 20:53
@ChipHurst What aboutres1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s]? And if you want to activate it,res1 /.[Zeta][s_] :> Zeta[s]
– theorist
Sep 4 at 0:41
add a comment |Â
up vote
15
down vote
accepted
You could Block Zeta so that it doesn't evaluate:
Block[Zeta=Inactive[Zeta],
Series[F[x],x,0,6]
] //TeXForm
$x+frac16 x^3 operatornameZeta(2,1)-frac16 x^4 operatornameZeta(3)+frac160 x^5
left(operatornameZeta(2,1)^2+9 operatornameZeta(4,1)right)+x^6 left(-frac130 operatornameZeta(3)
operatornameZeta(2,1)-frac2 operatornameZeta(5)15right)+Oleft(x^7right)$
answered Sep 3 at 20:28
Carl Woll
56.1k272146
You could postprocess the result withres /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].
– Chip Hurst
Sep 3 at 20:52
Also it's strangeInactive[Zeta]doesn't format in TraditionalForm withζ.
– Chip Hurst
Sep 3 at 20:53
@ChipHurst What aboutres1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s]? And if you want to activate it,res1 /.[Zeta][s_] :> Zeta[s]
– theorist
Sep 4 at 0:41
add a comment |Â
up vote
15
down vote
accepted
up vote
15
down vote
accepted
You could Block Zeta so that it doesn't evaluate:
Block[Zeta=Inactive[Zeta],
Series[F[x],x,0,6]
] //TeXForm
$x+frac16 x^3 operatornameZeta(2,1)-frac16 x^4 operatornameZeta(3)+frac160 x^5
left(operatornameZeta(2,1)^2+9 operatornameZeta(4,1)right)+x^6 left(-frac130 operatornameZeta(3)
operatornameZeta(2,1)-frac2 operatornameZeta(5)15right)+Oleft(x^7right)$
answered Sep 3 at 20:28
Carl Woll
56.1k272146
You could Block Zeta so that it doesn't evaluate:
Block[Zeta=Inactive[Zeta],
Series[F[x],x,0,6]
] //TeXForm
$x+frac16 x^3 operatornameZeta(2,1)-frac16 x^4 operatornameZeta(3)+frac160 x^5
left(operatornameZeta(2,1)^2+9 operatornameZeta(4,1)right)+x^6 left(-frac130 operatornameZeta(3)
operatornameZeta(2,1)-frac2 operatornameZeta(5)15right)+Oleft(x^7right)$
answered Sep 3 at 20:28
Carl Woll
56.1k272146
answered Sep 3 at 20:28
Carl Woll
56.1k272146
answered Sep 3 at 20:28
Carl Woll
56.1k272146
answered Sep 3 at 20:28
Carl Woll
56.1k272146
56.1k272146
You could postprocess the result withres /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].
– Chip Hurst
Sep 3 at 20:52
Also it's strangeInactive[Zeta]doesn't format in TraditionalForm withζ.
– Chip Hurst
Sep 3 at 20:53
@ChipHurst What aboutres1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s]? And if you want to activate it,res1 /.[Zeta][s_] :> Zeta[s]
– theorist
Sep 4 at 0:41
add a comment |Â
You could postprocess the result withres /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].
– Chip Hurst
Sep 3 at 20:52
Also it's strangeInactive[Zeta]doesn't format in TraditionalForm withζ.
– Chip Hurst
Sep 3 at 20:53
@ChipHurst What aboutres1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s]? And if you want to activate it,res1 /.[Zeta][s_] :> Zeta[s]
– theorist
Sep 4 at 0:41
You could postprocess the result with
res /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].– Chip Hurst
Sep 3 at 20:52
You could postprocess the result with
res /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s].– Chip Hurst
Sep 3 at 20:52
Also it's strange
Inactive[Zeta] doesn't format in TraditionalForm with ζ.– Chip Hurst
Sep 3 at 20:53
Also it's strange
Inactive[Zeta] doesn't format in TraditionalForm with ζ.– Chip Hurst
Sep 3 at 20:53
@ChipHurst What about
res1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s] ? And if you want to activate it, res1 /.[Zeta][s_] :> Zeta[s]– theorist
Sep 4 at 0:41
@ChipHurst What about
res1=res /. Inactive[Zeta][s_ , 1] :> [Zeta][s] /. Inactive[Zeta][s_ ] :> [Zeta][s] ? And if you want to activate it, res1 /.[Zeta][s_] :> Zeta[s]– theorist
Sep 4 at 0:41
add a comment |Â
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