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April 28 Information
Expression for a Gamma-like Function
Let Then for we have whose integral expression is I was wondering whether such expressions also exist for this generalized version of the function. —
79.113.194.139 (
talk) 04:30, 28 April 2014 (UTC)reply
Then that recursive relationship doesn't uniquely define . What's the boundary condition? The gamma function was motivated to coincide with the factorial. What is the motivation behind ?
203.45.159.248 (
talk) 09:59, 28 April 2014 (UTC)reply
Wow! Unbelievable as always, Slawomir! :-) If you could you also please explain the logic and/or intuition which helped you arrive at this expression ? Thanks! —
86.125.209.133 (
talk) 17:56, 28 April 2014 (UTC)reply
From the equation , I see that the solution should be something like . This doesn't quite work, so I try to write . Imposing the functional equation again gives which has as a solution. (Clearly there will be many functions solving this; I'm not sure what conditions are needed to ensure uniqueness.)
Sławomir Biały (
talk) 22:02, 28 April 2014 (UTC)reply
Resolved
A Space with Space-filling Dodecahedrons ???!!!...
The Cube is a Space-filling Solid...
The Dodecahedron is NOT!!!
Four Dodecahedrons have a empty Corner: 0xyz with 1,5o
Could it be a SPACE with Space-filling Dodecahedrons???...
Could it be a SPACE where the Icosahedron = 20 Tetrahedrons???...
I can Imagine them BUT could they be Calculated???...
Are these "Mistakes" say something about our Universe???...
Though if the order is more than 6 the vertices stick out beyond infinity. And as to {5,3,2}, how do you distinguish it from a
great sphere? —
Tamfang (
talk) 03:13, 29 April 2014 (UTC)reply
It's analogous to the pentagonal
dihedron {5,2}: the faces of the dodecahedra in {5,3,2} tile a great sphere, just as the sides of the pentagons in {5,2} tile a great circle.
Double sharp (
talk) 15:24, 29 April 2014 (UTC)reply
I don't think this says anything significant about our universe - Euclidean 3-space is only a local approximation of its actual geometry. There's only one space-filling fully regular honeycomb in 3-space - the cube, which has three sets of parallel faces. So if you want to consider the philosophical impact of this, I guess the question is "Why cubes?"
AlexTiefling (
talk) 15:57, 28 April 2014 (UTC)reply
You are probably thinking of the
rhombic dodecahedron. This is well-known to fill 3-space, and can be thought of as the 3-space analogy of the regular hexagon (which fills (tessellates) 2-space), though it is not
regular.
RomanSpa (
talk) 19:11, 28 April 2014 (UTC)reply
It's sufficiently clear, in my humble opinion, that that's not what he has in mind. —
Tamfang (
talk) 03:13, 29 April 2014 (UTC)reply
Here are two views of a curved space filled with regular dodecahedra
[1][2] — and two views of a space where 20 tetrahedra form an icosahedron
[3][4] —
Tamfang (
talk) 06:08, 29 April 2014 (UTC)reply
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
current reference desk pages.
April 28 Information
Expression for a Gamma-like Function
Let Then for we have whose integral expression is I was wondering whether such expressions also exist for this generalized version of the function. —
79.113.194.139 (
talk) 04:30, 28 April 2014 (UTC)reply
Then that recursive relationship doesn't uniquely define . What's the boundary condition? The gamma function was motivated to coincide with the factorial. What is the motivation behind ?
203.45.159.248 (
talk) 09:59, 28 April 2014 (UTC)reply
Wow! Unbelievable as always, Slawomir! :-) If you could you also please explain the logic and/or intuition which helped you arrive at this expression ? Thanks! —
86.125.209.133 (
talk) 17:56, 28 April 2014 (UTC)reply
From the equation , I see that the solution should be something like . This doesn't quite work, so I try to write . Imposing the functional equation again gives which has as a solution. (Clearly there will be many functions solving this; I'm not sure what conditions are needed to ensure uniqueness.)
Sławomir Biały (
talk) 22:02, 28 April 2014 (UTC)reply
Resolved
A Space with Space-filling Dodecahedrons ???!!!...
The Cube is a Space-filling Solid...
The Dodecahedron is NOT!!!
Four Dodecahedrons have a empty Corner: 0xyz with 1,5o
Could it be a SPACE with Space-filling Dodecahedrons???...
Could it be a SPACE where the Icosahedron = 20 Tetrahedrons???...
I can Imagine them BUT could they be Calculated???...
Are these "Mistakes" say something about our Universe???...
Though if the order is more than 6 the vertices stick out beyond infinity. And as to {5,3,2}, how do you distinguish it from a
great sphere? —
Tamfang (
talk) 03:13, 29 April 2014 (UTC)reply
It's analogous to the pentagonal
dihedron {5,2}: the faces of the dodecahedra in {5,3,2} tile a great sphere, just as the sides of the pentagons in {5,2} tile a great circle.
Double sharp (
talk) 15:24, 29 April 2014 (UTC)reply
I don't think this says anything significant about our universe - Euclidean 3-space is only a local approximation of its actual geometry. There's only one space-filling fully regular honeycomb in 3-space - the cube, which has three sets of parallel faces. So if you want to consider the philosophical impact of this, I guess the question is "Why cubes?"
AlexTiefling (
talk) 15:57, 28 April 2014 (UTC)reply
You are probably thinking of the
rhombic dodecahedron. This is well-known to fill 3-space, and can be thought of as the 3-space analogy of the regular hexagon (which fills (tessellates) 2-space), though it is not
regular.
RomanSpa (
talk) 19:11, 28 April 2014 (UTC)reply
It's sufficiently clear, in my humble opinion, that that's not what he has in mind. —
Tamfang (
talk) 03:13, 29 April 2014 (UTC)reply
Here are two views of a curved space filled with regular dodecahedra
[1][2] — and two views of a space where 20 tetrahedra form an icosahedron
[3][4] —
Tamfang (
talk) 06:08, 29 April 2014 (UTC)reply