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Proof involving generating function

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#sequences-and-series #elementary-number-theory #generating-functions
82
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Closed form for infinite series $\sum_{n=1}^\infty \prod_{j=1}^n \left[1-(\tfrac{j}{n}u+v)^2\right]^{-1} x^n$

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#sequences-and-series #special-functions #generating-functions #closed-form #gamma-function
73
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Closed form for $\sum_{i=1}^{n}\binom{n}{i}\frac{x^{i}}{i}$

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#summation #binomial-coefficients #generating-functions #closed-form
530
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3rd Factorial Moment of X ~ geo(p)

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#probability #expectation #generating-functions
296
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Find a closed formula for $ \sum _{k=0}^n k^2 5^k $

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#combinatorics #discrete-mathematics #generating-functions
176
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Generating series for powers of Fibonacci numbers

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#sequences-and-series #generating-functions #fibonacci-numbers
377
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Generalized generating function for binomial coefficients

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#binomial-coefficients #generating-functions
246
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Prove generating function of $a_n = (b+1)^n - b^n$

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#sequences-and-series #generating-functions
129
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Formal power series: $F_i(x)$ converges if and only if $\lim_{i\to\infty}deg(F_{i+1}(x)- F_i(x))=\infty.$

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#combinatorics #discrete-mathematics #generating-functions #formal-power-series
295
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Quadratic Fibonacci Sequence, Generating Function

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#sequences-and-series #generating-functions
76
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Combinatorics-Generating Functions( Kenneth Rosen ex 23a)

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#combinatorics #generating-functions
56
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Combinatorics-Exponential Generating Function(Kenneth Rosen ex 6.4 47e)

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#combinatorics #generating-functions
2.1k
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Why would you take the logarithmic derivative of a generating function?

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#combinatorics #generating-functions #oeis
351
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Proving a sum identity for the Bernoulli numbers

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#combinatorics #number-theory #generating-functions #constants
453
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How to find the distribution of the first hitting time of random walk on the line

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#probability #stochastic-processes #generating-functions #random-walk

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