Question

What is closed-form expression for $F(n)$ when $F(n)=F(n-1)+F(n-2)$ and $F(0)=a$,$F(1)=b$ and $a,b>0$?

score 2.2k · Answer 1 · 2013-02-21 12:47:22

2.2k

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What is closed-form expression for $F(n)$ when $F(n)=F(n-1)+F(n-2)$ and $F(0)=a$,$F(1)=b$ and $a,b>0$?

Published on 21 Feb 2013 - 12:47

score 1.1k · Answer 2 · 2013-02-22 23:47:23

1.1k

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Evaluate $\int_{0}^{\pi/4}x\ln^{2}(\sin(x))dx$

Published on 22 Feb 2013 - 23:47

score 4.6k · Answer 3 · 2026-04-11 10:06:55

4.6k

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Having a lot of trouble solving this recurrence with iteration and finding a closed form...

Published on 11 Apr 2026 - 10:06

score 2k · Answer 4 · 2026-04-11 02:07:06

2k

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Closed form for the sum of even fibonacci numbers?

Published on 11 Apr 2026 - 2:07

score 964 · Answer 5 · 2013-03-24 20:13:35

964

Views

Closed form sum of $\sum^{\infty}_{n=1} \frac{1}{3^n-1}$

Published on 24 Mar 2013 - 20:13

score 2k · Answer 6 · 2013-03-26 02:20:50

2k

Views

How can I find $\sum\limits_{n=0}^{\infty}\left(\frac{(-1)^n}{2n+1}\sum\limits_{k=0}^{2n}\frac{1}{2n+4k+3}\right)$?

Published on 26 Mar 2013 - 2:20

score 719 · Answer 7 · 2026-04-11 01:31:27

719

Views

Calculate an infinite continued fraction

Published on 11 Apr 2026 - 1:31

score 24k · Answer 8 · 2026-04-10 16:01:01

24k

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Finding the sum of series help: $\displaystyle\sum\limits_{n=1}^{\infty} (-9)^nx^n. $

Published on 10 Apr 2026 - 16:01

score 648 · Answer 9 · 2026-04-11 04:20:27

648

Views

Evaluating a nested summation

Published on 11 Apr 2026 - 4:20

score 189 · Answer 10 · 2020-07-31 14:27:21

189

Views

On hypergeometric square integral $\int_0^{\infty } \, _2F_1(a,b;c;-x){}^2 \, dx$

Published on 31 Jul 2020 - 14:27

score 48 · Answer 11 · 2026-04-11 05:07:14

48

Views

Which rational functions admit a closed-form summation?

Published on 11 Apr 2026 - 5:07

score 37 · Answer 12 · 2020-08-02 15:02:26

37

Views

Are there closed forms for $\Psi(z)=\sum_{n=1}^\infty \frac{1}{3^{n^z}} $ for $z \in \Bbb N/\{1,2\} $

Published on 02 Aug 2020 - 15:02

score 318 · Answer 13 · 2020-08-07 12:10:41

318

Views

Challenging limit: $\lim_{\alpha\to0^{+}}\left(\frac{1}{2\alpha}-\int_1^\infty\frac{dx}{\sinh(\pi\alpha x)\sqrt{x^2-1}}\right)$

Published on 07 Aug 2020 - 12:10

score 929 · Answer 14 · 2026-03-28 05:23:26

929

Views

Evaluating $\int_0^1\frac{\arctan x\ln\left(\frac{2x^2}{1+x^2}\right)}{1-x}dx$

Published on 28 Mar 2026 - 5:23

score 99 · Answer 15 · 2026-04-10 23:11:56

99

Views

Is it possible to express values such as $\sin^{-1}(\pi/12)$ without inverse trig functions?

Published on 10 Apr 2026 - 23:11

List Question

What is closed-form expression for $F(n)$ when $F(n)=F(n-1)+F(n-2)$ and $F(0)=a$,$F(1)=b$ and $a,b>0$?

Evaluate $\int_{0}^{\pi/4}x\ln^{2}(\sin(x))dx$

Having a lot of trouble solving this recurrence with iteration and finding a closed form...

Closed form for the sum of even fibonacci numbers?

Closed form sum of $\sum^{\infty}_{n=1} \frac{1}{3^n-1}$

How can I find $\sum\limits_{n=0}^{\infty}\left(\frac{(-1)^n}{2n+1}\sum\limits_{k=0}^{2n}\frac{1}{2n+4k+3}\right)$?

Calculate an infinite continued fraction

Finding the sum of series help: $\displaystyle\sum\limits_{n=1}^{\infty} (-9)^nx^n. $

Evaluating a nested summation

On hypergeometric square integral $\int_0^{\infty } \, _2F_1(a,b;c;-x){}^2 \, dx$

Which rational functions admit a closed-form summation?

Are there closed forms for $\Psi(z)=\sum_{n=1}^\infty \frac{1}{3^{n^z}} $ for $z \in \Bbb N/\{1,2\} $

Challenging limit: $\lim_{\alpha\to0^{+}}\left(\frac{1}{2\alpha}-\int_1^\infty\frac{dx}{\sinh(\pi\alpha x)\sqrt{x^2-1}}\right)$

Evaluating $\int_0^1\frac{\arctan x\ln\left(\frac{2x^2}{1+x^2}\right)}{1-x}dx$

Is it possible to express values such as $\sin^{-1}(\pi/12)$ without inverse trig functions?

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