Borel Bivariate Generating Function The Next CEO of Stack OverflowGenerating function of shifted Catalan NumbersGenerating function for reciprocals of Harmonic numbers?Generating function of Catalan numbers.Finding the generating function for the Catalan number sequenceCatalan numbers generating functionFinding generating function of binary tree using quadratic formula?Finding a closed formula for a generating function involving catalan numbersHow to find generating function of a sequenceGenerating function for the Catalan numbersGenerating Function For Catalan Numbers Type Sequence
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Borel Bivariate Generating Function
The Next CEO of Stack OverflowGenerating function of shifted Catalan NumbersGenerating function for reciprocals of Harmonic numbers?Generating function of Catalan numbers.Finding the generating function for the Catalan number sequenceCatalan numbers generating functionFinding generating function of binary tree using quadratic formula?Finding a closed formula for a generating function involving catalan numbersHow to find generating function of a sequenceGenerating function for the Catalan numbersGenerating Function For Catalan Numbers Type Sequence
$begingroup$
I want to prove the following statement:
$$ beta(t,x)=C(1+t,x)= frac C(1(1+t,x) 1-x(C(1+t)x) $$
Where $C(x)$ is the generating function for the Catalan Numbers and $ beta(x) $ is the Borel generating function.
I know I have to use the fact that $$ C(t,x)= frac C(tx) 1-xC(tx)$$
But unsure what other statements i need to use.
Any help would be great thanks.
combinatorics generating-functions catalan-numbers borel-sets
asked yesterday
frankfieldsfrankfields
165
$endgroup$
add a comment |
$begingroup$
I want to prove the following statement:
$$ beta(t,x)=C(1+t,x)= frac C(1(1+t,x) 1-x(C(1+t)x) $$
Where $C(x)$ is the generating function for the Catalan Numbers and $ beta(x) $ is the Borel generating function.
I know I have to use the fact that $$ C(t,x)= frac C(tx) 1-xC(tx)$$
But unsure what other statements i need to use.
Any help would be great thanks.
combinatorics generating-functions catalan-numbers borel-sets
asked yesterday
frankfieldsfrankfields
165
$endgroup$
$begingroup$
What is $beta$ exactly?
$endgroup$
– Phicar
yesterday
add a comment |
$begingroup$
I want to prove the following statement:
$$ beta(t,x)=C(1+t,x)= frac C(1(1+t,x) 1-x(C(1+t)x) $$
Where $C(x)$ is the generating function for the Catalan Numbers and $ beta(x) $ is the Borel generating function.
I know I have to use the fact that $$ C(t,x)= frac C(tx) 1-xC(tx)$$
But unsure what other statements i need to use.
Any help would be great thanks.
combinatorics generating-functions catalan-numbers borel-sets
asked yesterday
frankfieldsfrankfields
165
$endgroup$
I want to prove the following statement:
$$ beta(t,x)=C(1+t,x)= frac C(1(1+t,x) 1-x(C(1+t)x) $$
Where $C(x)$ is the generating function for the Catalan Numbers and $ beta(x) $ is the Borel generating function.
I know I have to use the fact that $$ C(t,x)= frac C(tx) 1-xC(tx)$$
But unsure what other statements i need to use.
Any help would be great thanks.
combinatorics generating-functions catalan-numbers borel-sets
combinatorics generating-functions catalan-numbers borel-sets
asked yesterday
frankfieldsfrankfields
165
asked yesterday
frankfieldsfrankfields
165
edited yesterday
frankfields
asked yesterday
frankfieldsfrankfields
165
asked yesterday
frankfieldsfrankfields
165
asked yesterday
frankfieldsfrankfields
165
165
$begingroup$
What is $beta$ exactly?
$endgroup$
– Phicar
yesterday
add a comment |
$begingroup$
What is $beta$ exactly?
$endgroup$
– Phicar
yesterday
$begingroup$
What is $beta$ exactly?
$endgroup$
– Phicar
yesterday
$begingroup$
What is $beta$ exactly?
$endgroup$
– Phicar
yesterday
add a comment |
0
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$begingroup$
What is $beta$ exactly?
$endgroup$
– Phicar
yesterday