Mixing
What does the function $E$ stand for in WolframAlpha's solution to this integral?
While trying to find the circumference of an ellipse, I came up with this result in Wolfram Alpha.
Equation: $dfrac{x^2}{a^2} + dfrac{y^2}{b^2} =1$
While trying to perform the definite integral, the computation timed out.
calculus integration definite-integrals indefinite-integrals
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
asked Jan 1 at 4:48
harshit54harshit54
346113
add a comment |
While trying to find the circumference of an ellipse, I came up with this result in Wolfram Alpha.
Equation: $dfrac{x^2}{a^2} + dfrac{y^2}{b^2} =1$
While trying to perform the definite integral, the computation timed out.
calculus integration definite-integrals indefinite-integrals
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
asked Jan 1 at 4:48
harshit54harshit54
346113
add a comment |
While trying to find the circumference of an ellipse, I came up with this result in Wolfram Alpha.
Equation: $dfrac{x^2}{a^2} + dfrac{y^2}{b^2} =1$
While trying to perform the definite integral, the computation timed out.
calculus integration definite-integrals indefinite-integrals
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
asked Jan 1 at 4:48
harshit54harshit54
346113
While trying to find the circumference of an ellipse, I came up with this result in Wolfram Alpha.
Equation: $dfrac{x^2}{a^2} + dfrac{y^2}{b^2} =1$
While trying to perform the definite integral, the computation timed out.
calculus integration definite-integrals indefinite-integrals
calculus integration definite-integrals indefinite-integrals
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
asked Jan 1 at 4:48
harshit54harshit54
346113
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
asked Jan 1 at 4:48
harshit54harshit54
346113
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
edited Jan 1 at 5:00
Eevee Trainer
5,3271835
5,3271835
asked Jan 1 at 4:48
harshit54harshit54
346113
asked Jan 1 at 4:48
harshit54harshit54
346113
asked Jan 1 at 4:48
harshit54harshit54
346113
346113
add a comment |
add a comment |
1 Answer
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active
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Wolfram Alpha usually specifies things like these below the equation and to the right, often linking to properties and definitions. Indeed, putting your integral into Wolfram Alpha:
The function $E$, here, refers to elliptic integrals of the second kind.
The site also links to its definition and a page on its properties and such.
Sadly, all this is way above my head, so in parsing said information I will likely be of absolutely no help to you. Good luck though!
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
3
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Wolfram Alpha usually specifies things like these below the equation and to the right, often linking to properties and definitions. Indeed, putting your integral into Wolfram Alpha:
The function $E$, here, refers to elliptic integrals of the second kind.
The site also links to its definition and a page on its properties and such.
Sadly, all this is way above my head, so in parsing said information I will likely be of absolutely no help to you. Good luck though!
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
3
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
add a comment |
Wolfram Alpha usually specifies things like these below the equation and to the right, often linking to properties and definitions. Indeed, putting your integral into Wolfram Alpha:
The function $E$, here, refers to elliptic integrals of the second kind.
The site also links to its definition and a page on its properties and such.
Sadly, all this is way above my head, so in parsing said information I will likely be of absolutely no help to you. Good luck though!
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
3
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
add a comment |
Wolfram Alpha usually specifies things like these below the equation and to the right, often linking to properties and definitions. Indeed, putting your integral into Wolfram Alpha:
The function $E$, here, refers to elliptic integrals of the second kind.
The site also links to its definition and a page on its properties and such.
Sadly, all this is way above my head, so in parsing said information I will likely be of absolutely no help to you. Good luck though!
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
Wolfram Alpha usually specifies things like these below the equation and to the right, often linking to properties and definitions. Indeed, putting your integral into Wolfram Alpha:
The function $E$, here, refers to elliptic integrals of the second kind.
The site also links to its definition and a page on its properties and such.
Sadly, all this is way above my head, so in parsing said information I will likely be of absolutely no help to you. Good luck though!
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
answered Jan 1 at 4:57
Eevee TrainerEevee Trainer
5,3271835
5,3271835
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
3
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
add a comment |
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
3
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Sorry. I was using the mobile version of the site. Thanks for the clarification.
– harshit54
Jan 1 at 5:18
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
Unfortunately I think even I won't be able to understand this.
– harshit54
Jan 1 at 5:25
3
3
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
It's not unsurprising that the arc length of an ellipse is expressed in terms of elliptic integrals. That's what elliptic integrals were originally invented for.
– Robert Israel
Jan 1 at 5:40
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
@RobertIsrael It was surprising for me because I thought that I will be able to get a formula for the circumference of an ellipse.
– harshit54
Jan 1 at 13:26
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
I mean, you have one. Just an unbelievably complicated one. :P
– Eevee Trainer
Jan 1 at 13:27
add a comment |
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