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Which type of counting problems are solved by hypergeometric function as generating function?

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#combinatorics #generating-functions
436
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Two questions about generating functions

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#sequences-and-series #generating-functions
498
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Closed form for coefficient of $x^N$ of $\frac{1}{(1-x^2)(1-x^3)(1-x^5)}$

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#combinatorics #generating-functions
269
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binomial expansion of $(1+x)^n \left(\dfrac{1}{x} -1\right)^m$

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#generating-functions
632
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Coefficient growth in the power series $\sum u_n z^n = e^{1/(1-z)}$?

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#complex-analysis #asymptotics #generating-functions
513
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Bernoulli and Euler numbers in some known series.

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#calculus #sequences-and-series #generating-functions #taylor-expansion
1.1k
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How to find generating function of cumulative sum?

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#number-theory #generating-functions
146
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Generating function with dependencies

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#combinatorics #generating-functions
1.3k
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Solving the recursion $3a_{n+1}=2(n+1)a_n+5(n+1)!$ via generating functions

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#recurrence-relations #power-series #generating-functions
76
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When and why does this series equivalence hold?

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#sequences-and-series #generating-functions
9.2k
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Why do engineers use the Z-transform and mathematicians use generating functions?

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#sequences-and-series #generating-functions #integral-transforms #z-transform
106
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How to solve a functional equation of the form $1-g(f(s))=m(1-g(s))$?

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#probability-theory #probability-distributions #generating-functions #functional-equations
1.6k
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Physical interpretation of the generating function for the Bessel functions.

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#complex-analysis #special-functions #intuition #generating-functions #physics
270
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Singularity of Generating Function

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#combinatorics #complex-analysis #generating-functions
2.3k
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The coefficient of $x^{18}$ in $(1+x^5+x^7)^{20}$

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#combinatorics #polynomials #generating-functions

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