Question

Cauchy product of alternating geometric series

score 68 · Answer 1 · 2026-02-23 12:54:15

68

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Cauchy product of alternating geometric series

Published on 23 Feb 2026 - 12:54

score 64 · Answer 2 · 2026-02-23 12:49:14

64

Views

Cauchy series "Product Like"

Published on 23 Feb 2026 - 12:49

score 59 · Answer 3 · 2026-02-23 12:56:57

59

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Can we write $\sum_{k=n}^\infty\sum_{\ell=0}^k a_\ell b_{k-\ell}$ as a product of series?

Published on 23 Feb 2026 - 12:56

score 174 · Answer 4 · 2026-02-23 12:58:42

174

Views

Why is the Cauchy product of the series $a_{n}:=b_{n}:=\dfrac{(-1)^n}{\sqrt{n+1}}$ diverging?

Published on 23 Feb 2026 - 12:58

score 130 · Answer 5 · 2026-02-23 12:51:48

130

Views

An expansion for $\ln^2\Gamma(x+1)$

Published on 23 Feb 2026 - 12:51

score 223 · Answer 6 · 2026-02-23 12:56:57

223

Views

How do you prove the Cauchy product (multiplication) of two infinite power series (generating functions) which have different exponents/indices?

Published on 23 Feb 2026 - 12:56

score 126 · Answer 7 · 2026-02-23 12:55:22

126

Views

What are other elegant counterexamples to the convergence of a Cauchy product?

Published on 23 Feb 2026 - 12:55

score 119 · Answer 8 · 2026-02-23 12:58:15

119

Views

Structure of product of two polynominals $\left( \sum_{k=0}^{n} a_k x^k \right) \cdot \left( \sum_{l=0}^{m} b_l y^l \right)$

Published on 23 Feb 2026 - 12:58

score 173 · Answer 9 · 2026-02-23 12:53:22

173

Views

What is the difference between a double infinite series and the Cauchy Product?

Published on 23 Feb 2026 - 12:53

score 193 · Answer 10 · 2026-02-23 12:58:40

193

Views

What is the Laurent series of $e^{z+z^{-1}}$? (Detailed derivation using Cauchy product of series)

Published on 23 Feb 2026 - 12:58

score 67 · Answer 11 · 2026-02-23 12:49:15

67

Views

Example of asymptotics for a discrete convolution

Published on 23 Feb 2026 - 12:49

score 331 · Answer 12 · 2026-02-23 12:56:56

331

Views

Can the Cauchy product of a conditionally convergent series with itself be absolutely convergent?

Published on 23 Feb 2026 - 12:56

score 91 · Answer 13 · 2026-02-23 12:53:00

91

Views

Show that $\sum_{\ell=0}^k \binom{2k+1}{2\ell} = 2^{2k}$

Published on 23 Feb 2026 - 12:53

score 113 · Answer 14 · 2026-02-23 12:55:21

113

Views

The Cauchy-product of these divergent, infinite series converges

Published on 23 Feb 2026 - 12:55

score 75 · Answer 15 · 2026-02-23 12:54:41

75

Views

Rearrange terms in products of power series

Published on 23 Feb 2026 - 12:54

List Question

Cauchy product of alternating geometric series

Cauchy series "Product Like"

Can we write $\sum_{k=n}^\infty\sum_{\ell=0}^k a_\ell b_{k-\ell}$ as a product of series?

Why is the Cauchy product of the series $a_{n}:=b_{n}:=\dfrac{(-1)^n}{\sqrt{n+1}}$ diverging?

An expansion for $\ln^2\Gamma(x+1)$

How do you prove the Cauchy product (multiplication) of two infinite power series (generating functions) which have different exponents/indices?

What are other elegant counterexamples to the convergence of a Cauchy product?

Structure of product of two polynominals $\left( \sum_{k=0}^{n} a_k x^k \right) \cdot \left( \sum_{l=0}^{m} b_l y^l \right)$

What is the difference between a double infinite series and the Cauchy Product?

What is the Laurent series of $e^{z+z^{-1}}$? (Detailed derivation using Cauchy product of series)

Example of asymptotics for a discrete convolution

Can the Cauchy product of a conditionally convergent series with itself be absolutely convergent?

Show that $\sum_{\ell=0}^k \binom{2k+1}{2\ell} = 2^{2k}$

The Cauchy-product of these divergent, infinite series converges

Rearrange terms in products of power series

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