Question

Complete this table of formulas for $_2F_1\big(a,b;c;u) =v $ with algebraic numbers $u,v$ and $a+b=c$?

score 224 · Answer 1 · 2026-03-27 20:31:18

224

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Complete this table of formulas for $_2F_1\big(a,b;c;u) =v $ with algebraic numbers $u,v$ and $a+b=c$?

Published on 27 Mar 2026 - 20:31

score 114 · Answer 2 · 2026-03-25 23:42:38

114

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Proving $\sqrt{x+y-x^2}+\sqrt{y+z-y^2}+\sqrt{z+w-z^2}+\sqrt{w+x-w^2}\le4\sqrt2-3$

Published on 25 Mar 2026 - 23:42

score 276 · Answer 3 · 2026-03-27 22:03:57

276

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How to show an infinite number of algebraic numbers $\alpha$ and $\beta$ for $_2F_1\left(\frac14,\frac14;\frac34;-\alpha\right)=\beta\,$?

Published on 27 Mar 2026 - 22:03

score 434 · Answer 4 · 2026-03-25 07:46:20

434

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On $_2F_1(\tfrac13,\tfrac23;\tfrac56;\tfrac{27}{32}) = \tfrac85$ and $_2F_1(\tfrac14,\tfrac34;\tfrac78;\tfrac{48}{49}) = \tfrac{\sqrt7}3(1+\sqrt2)$

Published on 25 Mar 2026 - 7:46

score 78 · Answer 5 · 2026-03-29 03:02:41

78

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How prove $\sum\limits_{cyc}\sqrt{a^2+b^2-c^2}\sqrt{a^2-b^2+c^2}\le ab+bc+ca$

Published on 29 Mar 2026 - 3:02

score 1.4k · Answer 6 · 2026-03-26 05:16:56

1.4k

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Rationalize the denominator with 4 terms $\frac{1}{1+\sqrt{12}-\sqrt[3]{3}-\sqrt[3]{9}}$

Published on 26 Mar 2026 - 5:16

score 144 · Answer 7 · 2026-03-31 14:23:22

144

Views

If $x = y$, $p$ = what?

Published on 31 Mar 2026 - 14:23

score 188 · Answer 8 · 2016-12-28 04:13:58

188

Views

Simplifying $9^{3/4}$, I get $3\sqrt[4]{9}$, but that's not the answer. Why?

Published on 28 Dec 2016 - 4:13

score 65 · Answer 9 · 2016-12-28 15:54:51

65

Views

Which limits involve computing square roots, Such as $\sqrt{n^2+6} -n$

Published on 28 Dec 2016 - 15:54

score 1.8k · Answer 10 · 2016-12-29 09:32:40

1.8k

Views

Why is the solution to $x-\sqrt 4=0$ not $x=\pm 2$?

Published on 29 Dec 2016 - 9:32

score 318 · Answer 11 · 2016-12-29 13:29:06

318

Views

Reducing square root fractions without calculator

Published on 29 Dec 2016 - 13:29

score 229 · Answer 12 · 2026-03-26 05:16:57

229

Views

Simplify $\frac{1}{\sqrt{-1+\sqrt{2}}}$

Published on 26 Mar 2026 - 5:16

score 316 · Answer 13 · 2016-12-29 19:04:40

316

Views

Solve system of equations with square roots and fractions

Published on 29 Dec 2016 - 19:04

score 382 · Answer 14 · 2016-12-30 18:35:38

382

Views

Prove $4-\sqrt{2}-\sqrt[3]{3}-\sqrt[5]{5} \gt 0$

Published on 30 Dec 2016 - 18:35

score 129 · Answer 15 · 2026-03-27 07:13:50

129

Views

Where can I find software to approximate very large square roots?

Published on 27 Mar 2026 - 7:13

List Question

Complete this table of formulas for $_2F_1\big(a,b;c;u) =v $ with algebraic numbers $u,v$ and $a+b=c$?

Proving $\sqrt{x+y-x^2}+\sqrt{y+z-y^2}+\sqrt{z+w-z^2}+\sqrt{w+x-w^2}\le4\sqrt2-3$

How to show an infinite number of algebraic numbers $\alpha$ and $\beta$ for $_2F_1\left(\frac14,\frac14;\frac34;-\alpha\right)=\beta\,$?

On $_2F_1(\tfrac13,\tfrac23;\tfrac56;\tfrac{27}{32}) = \tfrac85$ and $_2F_1(\tfrac14,\tfrac34;\tfrac78;\tfrac{48}{49}) = \tfrac{\sqrt7}3(1+\sqrt2)$

How prove $\sum\limits_{cyc}\sqrt{a^2+b^2-c^2}\sqrt{a^2-b^2+c^2}\le ab+bc+ca$

Rationalize the denominator with 4 terms $\frac{1}{1+\sqrt{12}-\sqrt[3]{3}-\sqrt[3]{9}}$

If $x = y$, $p$ = what?

Simplifying $9^{3/4}$, I get $3\sqrt[4]{9}$, but that's not the answer. Why?

Which limits involve computing square roots, Such as $\sqrt{n^2+6} -n$

Why is the solution to $x-\sqrt 4=0$ not $x=\pm 2$?

Reducing square root fractions without calculator

Simplify $\frac{1}{\sqrt{-1+\sqrt{2}}}$

Solve system of equations with square roots and fractions

Prove $4-\sqrt{2}-\sqrt[3]{3}-\sqrt[5]{5} \gt 0$

Where can I find software to approximate very large square roots?

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