User Pxx

7 votes

2 answers

120 views

Series expansion of $\text{Li}_3(1-x)$ at $x \sim 0$

asked Apr 13, 2022 at 13:37

4 votes

2 answers

160 views

Integral $I(\tau_1,a,b) = \int_{\tau_1}^\infty d\tau_2\ \frac{1}{b^2 + \tau_2^2} \left(\pi - 2 \tan^{-1} \frac{\tau_2}{a} \right)^2$

asked May 17, 2020 at 6:54

4 votes

1 answer

253 views

Can this integral be expanded as a power series?

asked Jul 5, 2020 at 17:28

4 votes

1 answer

181 views

What is the closed form of the sequence $\{-\frac12,\frac19,\frac{13}{100},\frac{71}{588},\frac{71}{648},\frac{1447}{14520},\frac{617}{6760},...\}$?

asked Jul 18, 2020 at 13:16

3 votes

1 answer

88 views

Challenge: what is the closed form of this function?

asked Mar 9, 2020 at 21:23

3 votes

2 answers

630 views

Electric field lines between surfaces of hollow sphere

asked Nov 17, 2016 at 14:42

3 votes

0 answers

60 views

How can I show that this integral is zero?

asked Oct 5, 2019 at 19:24

2 votes

2 answers

816 views

How to solve integrals with $3$ Feynman parameters?

asked Oct 3, 2019 at 19:02

2 votes

0 answers

59 views

Why does the divergence in my integral has a change of type?

asked Nov 8, 2019 at 15:49

2 votes

1 answer

42 views

How does this function involving sets read?

asked Oct 21, 2015 at 19:53

2 votes

3 answers

4k views

What is the difference between cartesian product and intersection?

asked Oct 22, 2015 at 20:43

2 votes

1 answer

125 views

How can I compute this integral involving $\Gamma$-functions?

asked Mar 12, 2020 at 11:47

2 votes

0 answers

71 views

Is this integral always valid?

asked Oct 23, 2019 at 21:17

2 votes

0 answers

74 views

Can I bring this integral into a form involving known functions?

asked Jan 30, 2020 at 10:48

2 votes

1 answer

102 views

What is the closed form of the sequence $\left\lbrace 32, 422, 3406 , 22426,131995, ... \right\rbrace$

asked Jul 26, 2020 at 9:17

2 votes

1 answer

35 views

Closed form for this power series looking like an hypergeometric?

asked Apr 25, 2021 at 9:22

1 vote

0 answers

48 views

Is this integration by parts allowed?

asked May 10, 2020 at 18:36

1 vote

1 answer

68 views

Proof that the set of Pochhammer numbers satisfies Benford's law

asked Dec 13, 2020 at 21:12

1 vote

1 answer

36 views

Solve a simple complex partial differential equation

asked Apr 26, 2020 at 16:11

1 vote

2 answers

550 views

How to show that a set operation is associative?

asked Oct 22, 2015 at 21:30

1 vote

2 answers

66 views

Ambiguity in the limit comparison test for integrability

asked Apr 12, 2016 at 16:13

1 vote

2 answers

181 views

Why is this differential equation an exact differential equation?

asked Dec 3, 2016 at 20:03

1 vote

0 answers

26 views

Is there a coordinate system in which this integral would become easier?

asked Nov 11, 2019 at 15:51

1 vote

1 answer

115 views

Can I rewrite this expression with a Dirac $\delta$-function?

asked Nov 28, 2019 at 11:13

1 vote

0 answers

24 views

Can $\text{Li}_2(x/y)$ be expressed as a sum of other $\text{Li}_2$?

asked Oct 8, 2022 at 19:32

0 votes

0 answers

44 views

Evaluate complicated $2d$-integral of the type $\int d^2 x \frac{1}{f(\vec{x})} \arccos(g(\vec{x}))$

asked Jan 12, 2020 at 16:14

0 votes

1 answer

471 views

Partial fraction decomposition when a power is negative

asked Oct 21, 2019 at 15:41

0 votes

1 answer

550 views

When is an image produced by a lens sharp? (optics)

asked Nov 25, 2016 at 17:36

0 votes

2 answers

1k views

Lens design using the matrix method (three lenses)

asked Nov 26, 2016 at 12:13

0 votes

1 answer

1k views

Proving that the product of contravariant and covariant vectors is Lorentz-invariant

asked Dec 21, 2016 at 15:30

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38 Questions

Series expansion of $\text{Li}_3(1-x)$ at $x \sim 0$

Integral $I(\tau_1,a,b) = \int_{\tau_1}^\infty d\tau_2\ \frac{1}{b^2 + \tau_2^2} \left(\pi - 2 \tan^{-1} \frac{\tau_2}{a} \right)^2$

Can this integral be expanded as a power series?

What is the closed form of the sequence $\{-\frac12,\frac19,\frac{13}{100},\frac{71}{588},\frac{71}{648},\frac{1447}{14520},\frac{617}{6760},...\}$?

Challenge: what is the closed form of this function?

Electric field lines between surfaces of hollow sphere

How can I show that this integral is zero?

How to solve integrals with $3$ Feynman parameters?

Why does the divergence in my integral has a change of type?

How does this function involving sets read?

What is the difference between cartesian product and intersection?

How can I compute this integral involving $\Gamma$-functions?

Is this integral always valid?

Can I bring this integral into a form involving known functions?

What is the closed form of the sequence $\left\lbrace 32, 422, 3406 , 22426,131995, ... \right\rbrace$

Closed form for this power series looking like an hypergeometric?

Is this integration by parts allowed?

Proof that the set of Pochhammer numbers satisfies Benford's law

Solve a simple complex partial differential equation

How to show that a set operation is associative?

Ambiguity in the limit comparison test for integrability

Why is this differential equation an exact differential equation?

Is there a coordinate system in which this integral would become easier?

Can I rewrite this expression with a Dirac $\delta$-function?

Can $\text{Li}_2(x/y)$ be expressed as a sum of other $\text{Li}_2$?

Evaluate complicated $2d$-integral of the type $\int d^2 x \frac{1}{f(\vec{x})} \arccos(g(\vec{x}))$

Partial fraction decomposition when a power is negative

When is an image produced by a lens sharp? (optics)

Lens design using the matrix method (three lenses)

Proving that the product of contravariant and covariant vectors is Lorentz-invariant