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Legendre polynomial expansion

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#calculus #sequences-and-series #generating-functions #recursive-algorithms #legendre-polynomials
129
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Counting the number of partitions such that every part is divisible by $k$.

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#combinatorics #discrete-mathematics #generating-functions #integer-partitions
68
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Which Schauder bases of $F[[x]]$ have the multiplication property?

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#combinatorics #generating-functions #topological-vector-spaces #formal-power-series #schauder-basis
61
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Exponential generating function in the case of a singular symbol

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#combinatorics #generating-functions
98
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Ordinary Power series

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#sequences-and-series #generating-functions
59
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How to calculate $(\sum_{n=0}^{\infty} a_n x^n )^3$?

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#real-analysis #summation #generating-functions
75
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Find a closed formula for $\sum_{n\geq 0} f(n)x^n.$

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#discrete-mathematics #recurrence-relations #generating-functions #closed-form
36
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Interesting properties of functions whose derivatives at a point form a given sequence?

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#real-analysis #sequences-and-series #analysis #generating-functions
47
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Generating function of some Apéry's series

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#power-series #generating-functions
178
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Solving recurrence using EGF

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#recurrence-relations #generating-functions
432
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On integration over distribution.

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#probability #integration #generating-functions #machine-learning #data-analysis
696
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Partitions of $n$ into even number of parts versus into odd number of parts

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#combinatorics #discrete-mathematics #generating-functions #integer-partitions
40
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Are there any applications of analytic properties of generating functions which don't require complex analysis?

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#real-analysis #complex-analysis #generating-functions
66
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Find the number of solutions $x_1+x_2+\dots+x_n=r$ where each variable is either $0$ or $1$.

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#combinatorics #generating-functions
59
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The number of binary sequences generated by a parity map from all integer partitions of $n$ and their permutations

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#combinatorics #generating-functions #integer-partitions #combinatorial-proofs

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