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How do you obtain the generating function from a summation?

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#sequences-and-series #discrete-mathematics #summation #recurrence-relations #generating-functions
34
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Special form for Gaussian hypergeometric function with a=1 and z=-1

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#combinatorics #generating-functions #hypergeometric-function
177
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Solving a particular recursion

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#sequences-and-series #recurrence-relations #generating-functions #recursion
84
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On combinatoric equality $\sum_{i=1}^{n-1}{n\choose i} i^{i-1} (n-i)^{n-i-1}=2(n-1)n^{n-2}$

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#combinatorics #summation #binomial-coefficients #generating-functions #lambert-w
46
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Expression for product of binomial coefficients

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#binomial-coefficients #generating-functions
288
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Closed form of $\sum _{n=2}^{\infty }\zeta (n)^2 z^n$

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#definite-integrals #generating-functions #riemann-zeta #bessel-functions #harmonic-numbers
112
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Strange Bijection in $\mathbb{Z}/(2^n-1)\mathbb{Z}$

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#number-theory #generating-functions
123
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Series of product of legendre polynomials with shifted degree

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#power-series #generating-functions #quantum-mechanics #legendre-polynomials #hadamard-product
59
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How to apply the Transfer Theorem on $\frac{z}{1-z-z^2}$ and $\frac{1+z-\sqrt{z^2-6z+1}}{4}$?

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#combinatorics #generating-functions #analytic-combinatorics
71
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Why does this random walk generating function admit an analytic continuation?

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#combinatorics #complex-analysis #generating-functions #random-walk
132
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Combinatorial interpretation of $\prod^\infty_{k=0}\left( 1+x^{2^k}\right) = \frac{1}{1-x}$

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#combinatorics #generating-functions #infinite-product #combinatorial-proofs
144
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About generating functions and convergence of power series. ("Introduction to Combinatorial Mathematics" by C. L. Liu.)

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#combinatorics #convergence-divergence #generating-functions
55
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Generating function does not imply uncorrelation.

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#probability #combinatorics #generating-functions
82
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Solving another discrete ODE with generating function

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#ordinary-differential-equations #discrete-mathematics #recurrence-relations #generating-functions
57
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Generating functions for ratios of sequences

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#combinatorics #generating-functions

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