Question

What is the Taylor series expansion of Incomplete Elliptical Integral Second Kind (namely $E(\phi,k)$ and its inverse $E^{-1}(\phi,k)$?

score 154 · Answer 1 · 2019-09-05 12:37:42

154

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What is the Taylor series expansion of Incomplete Elliptical Integral Second Kind (namely $E(\phi,k)$ and its inverse $E^{-1}(\phi,k)$?

Published on 05 Sep 2019 - 12:37

score 430 · Answer 2 · 2019-09-06 09:37:10

430

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Elliptic integrals using complex analysis

Published on 06 Sep 2019 - 9:37

score 783 · Answer 3 · 2019-09-10 16:58:30

783

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Integrate $\int \frac{\sqrt x}{\sqrt {a^2-x^2}}dx$

Published on 10 Sep 2019 - 16:58

score 446 · Answer 4 · 2019-09-20 13:11:37

446

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Elliptic integrals: derivation of the imaginary-modulus transformation

Published on 20 Sep 2019 - 13:11

score 772 · Answer 5 · 2014-03-13 07:30:44

772

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Formula for $\int_0^\infty \frac{\log(1+x^2)}{\sqrt{(a^2+x^2)(b^2+x^2)}}dx$

Published on 13 Mar 2014 - 7:30

score 252 · Answer 6 · 2014-04-07 01:07:29

252

Views

Relationship between elliptic integrals of first and second order.

Published on 07 Apr 2014 - 1:07

score 2.1k · Answer 7 · 2014-04-08 15:01:43

2.1k

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How to get arc-length of polar function $r= 4(1-\sin{\phi})$?

Published on 08 Apr 2014 - 15:01

score 535 · Answer 8 · 2014-04-13 08:49:38

535

Views

Prove that these two curves have the same length

Published on 13 Apr 2014 - 8:49

score 454 · Answer 9 · 2014-04-26 12:01:06

454

Views

Infinite series representation of elliptic integrals $F(k,\phi)$ and $E(k,\phi).$

Published on 26 Apr 2014 - 12:01

score 501 · Answer 10 · 2014-04-27 12:35:44

501

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Does $\int_0^{2 \pi} \sqrt{1-(a+b \sin\phi)^2} d\phi $ have a closed form in terms of elliptic integrals?

Published on 27 Apr 2014 - 12:35

score 565 · Answer 11 · 2014-05-01 16:36:03

565

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The closed form of $\sum_{n=0}^{\infty} \arcsin\bigl(\frac{1}{e^n}\bigr)$

Published on 01 May 2014 - 16:36

score 3.8k · Answer 12 · 2014-05-01 22:06:12

3.8k

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TaylorSeries of complete elliptic integral of the first kind

Published on 01 May 2014 - 22:06

score 1.4k · Answer 13 · 2014-05-04 22:12:00

1.4k

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Fundamental period of the Weierstrass $\wp$ elliptic function?

Published on 04 May 2014 - 22:12

score 361 · Answer 14 · 2014-05-06 15:42:43

361

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Closed form of $\sum_{n=1}^\infty(-1)^{n+1} \frac xn \ln\left(1+\frac xn\right), \quad x \in (0,1)$

Published on 06 May 2014 - 15:42

score 158 · Answer 15 · 2014-05-08 16:14:29

158

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Expression of $2\int_{0}^{\frac{1}{r_{0}}}\frac{du}{\sqrt{\frac{r_{0}-r_{s}}{r_{0}^{3}}-u^{2}\left(1-u r_{s}\right)}}$ in terms of elliptic integrals

Published on 08 May 2014 - 16:14

List Question

What is the Taylor series expansion of Incomplete Elliptical Integral Second Kind (namely $E(\phi,k)$ and its inverse $E^{-1}(\phi,k)$?

Elliptic integrals using complex analysis

Integrate $\int \frac{\sqrt x}{\sqrt {a^2-x^2}}dx$

Elliptic integrals: derivation of the imaginary-modulus transformation

Formula for $\int_0^\infty \frac{\log(1+x^2)}{\sqrt{(a^2+x^2)(b^2+x^2)}}dx$

Relationship between elliptic integrals of first and second order.

How to get arc-length of polar function $r= 4(1-\sin{\phi})$?

Prove that these two curves have the same length

Infinite series representation of elliptic integrals $F(k,\phi)$ and $E(k,\phi).$

Does $\int_0^{2 \pi} \sqrt{1-(a+b \sin\phi)^2} d\phi $ have a closed form in terms of elliptic integrals?

The closed form of $\sum_{n=0}^{\infty} \arcsin\bigl(\frac{1}{e^n}\bigr)$

TaylorSeries of complete elliptic integral of the first kind

Fundamental period of the Weierstrass $\wp$ elliptic function?

Closed form of $\sum_{n=1}^\infty(-1)^{n+1} \frac xn \ln\left(1+\frac xn\right), \quad x \in (0,1)$

Expression of $2\int_{0}^{\frac{1}{r_{0}}}\frac{du}{\sqrt{\frac{r_{0}-r_{s}}{r_{0}^{3}}-u^{2}\left(1-u r_{s}\right)}}$ in terms of elliptic integrals

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