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Generalized Harmonic Number Summation $ \sum_{n=1}^{\infty} {2^{-n}}{(H_{n}^{(2)})^2}$

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#real-analysis #sequences-and-series #generating-functions #harmonic-numbers
108
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Finding the generating function of a recurrence relation in dependence of a variable

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#discrete-mathematics #recurrence-relations #generating-functions
150
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How do I get a sequence from a generating function?

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#sequences-and-series #number-theory #polynomials #generating-functions
44
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Deriving the sequence if the generating function is irreducible?

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#sequences-and-series #number-theory #generating-functions #partial-fractions
61
Views

Is $G(\alpha s)/G(\alpha)$ a probability generating function

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#probability #generating-functions
147
Views

Question About Cauchy Product;

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#sequences-and-series #power-series #taylor-expansion #generating-functions #cauchy-product
969
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Probability generating function of some "random walk"

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#probability #generating-functions #random-walk
87
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Transforming generating functions into algorithms that generate combinatorial objects

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#combinatorics #algorithms #generating-functions #trees
1.4k
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Deriving sum of powers formula using generating functions

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#sequences-and-series #number-theory #summation #recurrence-relations #generating-functions
112
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Generating function for $\sum_{n=0}^{\infty} n^{p} x^n$

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#sequences-and-series #number-theory #summation #recurrence-relations #generating-functions
27.1k
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How to Multiply Two Infinite Series Correctly?

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#generating-functions
60
Views

want to check answer given in my book is correct or not

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#taylor-expansion #generating-functions #binomial-theorem
64
Views

How to formally use Taylor expansions for $n$th derivatives and generating functions?

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#number-theory #derivatives #power-series #generating-functions #catalan-numbers
378
Views

Generating function for $\sum_{n=0}^{\infty} n^k x^n$

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#sequences-and-series #number-theory #power-series #generating-functions #closed-form
3.5k
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How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

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#combinatorics #binomial-coefficients #generating-functions #combinatorial-proofs

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