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 157 · Answer 1 · 2026-04-16 12:26:31

157

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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 16 Apr 2026 - 12:26

score 433 · Answer 2 · 2026-04-08 17:30:45

433

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Elliptic integrals using complex analysis

Published on 08 Apr 2026 - 17:30

score 785 · Answer 3 · 2026-04-14 21:42:13

785

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

Published on 14 Apr 2026 - 21:42

score 449 · Answer 4 · 2026-04-13 06:14:40

449

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Elliptic integrals: derivation of the imaginary-modulus transformation

Published on 13 Apr 2026 - 6:14

score 775 · Answer 5 · 2026-04-16 18:07:09

775

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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 16 Apr 2026 - 18:07

score 255 · Answer 6 · 2026-04-12 20:22:32

255

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Relationship between elliptic integrals of first and second order.

Published on 12 Apr 2026 - 20:22

score 2.1k · Answer 7 · 2026-04-13 14:00:20

2.1k

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

Published on 13 Apr 2026 - 14:00

score 538 · Answer 8 · 2026-04-16 06:19:19

538

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Prove that these two curves have the same length

Published on 16 Apr 2026 - 6:19

score 457 · Answer 9 · 2026-04-17 14:12:56

457

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

Published on 17 Apr 2026 - 14:12

score 504 · Answer 10 · 2026-04-15 13:05:29

504

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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 15 Apr 2026 - 13:05

score 568 · Answer 11 · 2026-04-15 23:22:48

568

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

Published on 15 Apr 2026 - 23:22

score 3.8k · Answer 12 · 2026-04-16 19:17:58

3.8k

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TaylorSeries of complete elliptic integral of the first kind

Published on 16 Apr 2026 - 19:17

score 1.4k · Answer 13 · 2026-04-17 03:01:41

1.4k

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

Published on 17 Apr 2026 - 3:01

score 364 · Answer 14 · 2026-04-14 08:04:08

364

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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 14 Apr 2026 - 8:04

score 161 · Answer 15 · 2026-04-16 05:21:42

161

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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 16 Apr 2026 - 5:21

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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