What is this number called?
Sorry, pretty awful title to describe my question.
Sometimes I like playing around with series expansions for certain functions on Mathematica, and if the function has a singularity at a point $b$, sometimes the little suggestion box will say something like "Series around $ x=b$" and will give me a series expansion around that point. I know this number is special, I don't know why, but sometimes at that series expansion it will have the obvious singularity, like $dfrac{1}{x-b}$ and then after that a finite number followed by more powers of $x$ with coefficients.
What is that finite number called?
calculus sequences-and-series terminology
edited Aug 11 '15 at 9:50
joriki
170k10183343
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
|
show 5 more comments
Sorry, pretty awful title to describe my question.
Sometimes I like playing around with series expansions for certain functions on Mathematica, and if the function has a singularity at a point $b$, sometimes the little suggestion box will say something like "Series around $ x=b$" and will give me a series expansion around that point. I know this number is special, I don't know why, but sometimes at that series expansion it will have the obvious singularity, like $dfrac{1}{x-b}$ and then after that a finite number followed by more powers of $x$ with coefficients.
What is that finite number called?
calculus sequences-and-series terminology
edited Aug 11 '15 at 9:50
joriki
170k10183343
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
What number?${}$
– Git Gud
Aug 11 '15 at 9:41
The coefficient of $(x-b)^0$? Is it the residue?
– Empy2
Aug 11 '15 at 9:45
I have an example: wolframalpha.com/input/?i=1%2F%28s*%28s%2B1%29%29 If you go to where it says Series expansion at s=0, it will give 1/s-1+s+.....i'm talking about the -1 in that series expansion. Its not always -1, and sometimes there is no constant term at a series expansion around a singularity, but is there a name for the constant term in a series expansion for a function around its singularity?
– Dave huff
Aug 11 '15 at 9:45
Don't you mean $(x-b)^{-1}$ ?
– Yves Daoust
Aug 11 '15 at 9:46
My bad on the description, its not a coefficient on any of the series terms, its a constant number, there is no x multiplying it.
– Dave huff
Aug 11 '15 at 9:47
|
show 5 more comments
Sorry, pretty awful title to describe my question.
Sometimes I like playing around with series expansions for certain functions on Mathematica, and if the function has a singularity at a point $b$, sometimes the little suggestion box will say something like "Series around $ x=b$" and will give me a series expansion around that point. I know this number is special, I don't know why, but sometimes at that series expansion it will have the obvious singularity, like $dfrac{1}{x-b}$ and then after that a finite number followed by more powers of $x$ with coefficients.
What is that finite number called?
calculus sequences-and-series terminology
edited Aug 11 '15 at 9:50
joriki
170k10183343
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
Sorry, pretty awful title to describe my question.
Sometimes I like playing around with series expansions for certain functions on Mathematica, and if the function has a singularity at a point $b$, sometimes the little suggestion box will say something like "Series around $ x=b$" and will give me a series expansion around that point. I know this number is special, I don't know why, but sometimes at that series expansion it will have the obvious singularity, like $dfrac{1}{x-b}$ and then after that a finite number followed by more powers of $x$ with coefficients.
What is that finite number called?
calculus sequences-and-series terminology
calculus sequences-and-series terminology
edited Aug 11 '15 at 9:50
joriki
170k10183343
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
edited Aug 11 '15 at 9:50
joriki
170k10183343
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
edited Aug 11 '15 at 9:50
joriki
170k10183343
edited Aug 11 '15 at 9:50
joriki
170k10183343
edited Aug 11 '15 at 9:50
joriki
170k10183343
170k10183343
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
asked Aug 11 '15 at 9:40
Dave huffDave huff
478211
478211
What number?${}$
– Git Gud
Aug 11 '15 at 9:41
The coefficient of $(x-b)^0$? Is it the residue?
– Empy2
Aug 11 '15 at 9:45
I have an example: wolframalpha.com/input/?i=1%2F%28s*%28s%2B1%29%29 If you go to where it says Series expansion at s=0, it will give 1/s-1+s+.....i'm talking about the -1 in that series expansion. Its not always -1, and sometimes there is no constant term at a series expansion around a singularity, but is there a name for the constant term in a series expansion for a function around its singularity?
– Dave huff
Aug 11 '15 at 9:45
Don't you mean $(x-b)^{-1}$ ?
– Yves Daoust
Aug 11 '15 at 9:46
My bad on the description, its not a coefficient on any of the series terms, its a constant number, there is no x multiplying it.
– Dave huff
Aug 11 '15 at 9:47
|
show 5 more comments
What number?${}$
– Git Gud
Aug 11 '15 at 9:41
The coefficient of $(x-b)^0$? Is it the residue?
– Empy2
Aug 11 '15 at 9:45
I have an example: wolframalpha.com/input/?i=1%2F%28s*%28s%2B1%29%29 If you go to where it says Series expansion at s=0, it will give 1/s-1+s+.....i'm talking about the -1 in that series expansion. Its not always -1, and sometimes there is no constant term at a series expansion around a singularity, but is there a name for the constant term in a series expansion for a function around its singularity?
– Dave huff
Aug 11 '15 at 9:45
Don't you mean $(x-b)^{-1}$ ?
– Yves Daoust
Aug 11 '15 at 9:46
My bad on the description, its not a coefficient on any of the series terms, its a constant number, there is no x multiplying it.
– Dave huff
Aug 11 '15 at 9:47
What number?${}$
– Git Gud
Aug 11 '15 at 9:41
What number?${}$
– Git Gud
Aug 11 '15 at 9:41
The coefficient of $(x-b)^0$? Is it the residue?
– Empy2
Aug 11 '15 at 9:45
The coefficient of $(x-b)^0$? Is it the residue?
– Empy2
Aug 11 '15 at 9:45
I have an example: wolframalpha.com/input/?i=1%2F%28s*%28s%2B1%29%29 If you go to where it says Series expansion at s=0, it will give 1/s-1+s+.....i'm talking about the -1 in that series expansion. Its not always -1, and sometimes there is no constant term at a series expansion around a singularity, but is there a name for the constant term in a series expansion for a function around its singularity?
– Dave huff
Aug 11 '15 at 9:45
I have an example: wolframalpha.com/input/?i=1%2F%28s*%28s%2B1%29%29 If you go to where it says Series expansion at s=0, it will give 1/s-1+s+.....i'm talking about the -1 in that series expansion. Its not always -1, and sometimes there is no constant term at a series expansion around a singularity, but is there a name for the constant term in a series expansion for a function around its singularity?
– Dave huff
Aug 11 '15 at 9:45
Don't you mean $(x-b)^{-1}$ ?
– Yves Daoust
Aug 11 '15 at 9:46
Don't you mean $(x-b)^{-1}$ ?
– Yves Daoust
Aug 11 '15 at 9:46
My bad on the description, its not a coefficient on any of the series terms, its a constant number, there is no x multiplying it.
– Dave huff
Aug 11 '15 at 9:47
My bad on the description, its not a coefficient on any of the series terms, its a constant number, there is no x multiplying it.
– Dave huff
Aug 11 '15 at 9:47
|
show 5 more comments
1 Answer
1
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This is usually called the constant term. See e.g. mathwords.
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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oldest
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votes
This is usually called the constant term. See e.g. mathwords.
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
add a comment |
This is usually called the constant term. See e.g. mathwords.
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
add a comment |
This is usually called the constant term. See e.g. mathwords.
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
This is usually called the constant term. See e.g. mathwords.
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
answered Aug 11 '15 at 9:50
jorikijoriki
170k10183343
170k10183343
add a comment |
add a comment |
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What number?${}$
– Git Gud
Aug 11 '15 at 9:41
The coefficient of $(x-b)^0$? Is it the residue?
– Empy2
Aug 11 '15 at 9:45
I have an example: wolframalpha.com/input/?i=1%2F%28s*%28s%2B1%29%29 If you go to where it says Series expansion at s=0, it will give 1/s-1+s+.....i'm talking about the -1 in that series expansion. Its not always -1, and sometimes there is no constant term at a series expansion around a singularity, but is there a name for the constant term in a series expansion for a function around its singularity?
– Dave huff
Aug 11 '15 at 9:45
Don't you mean $(x-b)^{-1}$ ?
– Yves Daoust
Aug 11 '15 at 9:46
My bad on the description, its not a coefficient on any of the series terms, its a constant number, there is no x multiplying it.
– Dave huff
Aug 11 '15 at 9:47