[Z]etas defined: a challenge to Aatu, Bacle, and Adam Kerman to derive

<math><semantics><mrow> <msqrt><mrow><mn>2</mn></mrow></
msqrt><mrow><mo>&middot;</mo></mrow><msqrt><mrow><mn>5</mn></mrow></
msqrt></mrow><annotation-xml encoding='MathML-Content'><apply><times/
><apply><root/><cn type = 'integer'>5</cn></apply><apply><root/><cn
type = 'integer'>2</cn></apply></apply></annotation-xml></semantics></
math>
Musatov
ExpressionsName Input
z[0]
(abs(((-2) + (5)^(1/2))) * (2)^(1/2))
z[1]
(2)^(1/2)
z[2]
((5)^(1/2) * (2)^(1/2))
z[3]
[t, (t * (-3))]
z[4]
((-10) + (X)^(2) + (Y)^(2))
z[5]
(PI * 10)
z[6]
(PI * (5)^(1/2) * (2)^(1/2) * 2)
z[7]
3.16227766016838
z[8]
(abs((2 + ((5)^(1/2) * (-1)))) * (2)^(1/2))
z[9]
0.333850535422189
unnamed1
ExpressionsName Input
z[0]
Content | Presentation | Both
<math> <semantics> <mrow> <msqrt> <mrow> <mn> 2</mn> </mrow> </msqrt>
<mrow> <mo> ·</mo> </mrow> <mfenced open = '|' close = '|'> <mrow>
<mrow> <mo> -</mo> <mn> 2</mn> <mo> + </mo> </mrow> <msqrt> <mrow>
<mn> 5</mn> </mrow> </msqrt> </mrow> </mfenced> </mrow> <annotation-
xml encoding='MathML-Content'> <apply> <times/> <apply> <abs/> <apply>
<plus/> <cn type = 'integer'> (-2)</cn> <apply> <root/> <cn type =
'integer'> 5</cn> </apply> </apply> </apply> <apply> <root/> <cn type
= 'integer'> 2</cn> </apply> </apply> </annotation-xml> </semantics> </
math>
z[1]
Content | Presentation | Both
<math> <semantics> <msqrt> <mrow> <mn> 2</mn> </mrow> </msqrt>
<annotation-xml encoding='MathML-Content'> <apply> <root/> <cn type =
'integer'> 2</cn> </apply> </annotation-xml> </semantics> </math>
z[2]
Content | Presentation | Both
<math> <semantics> <mrow> <msqrt> <mrow> <mn> 2</mn> </mrow> </msqrt>
<mrow> <mo> ·</mo> </mrow> <msqrt> <mrow> <mn> 5</mn> </mrow> </msqrt>
</mrow> <annotation-xml encoding='MathML-Content'> <apply> <times/>
<apply> <root/> <cn type = 'integer'> 5</cn> </apply> <apply> <root/>
<cn type = 'integer'> 2</cn> </apply> </apply> </annotation-xml> </
semantics> </math>
z[3]
Content | Presentation | Both
<math> <semantics> <mfenced> <mtable> <mtr> <mtd> <mrow> <mi> t</mi> </
mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo> -</mo> <mn> 3</mn> <mo> ·</
mo> <mi> t</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <annotation-
xml encoding='MathML-Content'> <vector> <ci variable-value = "1"> t</
ci> <apply> <times/> <ci variable-value = "1"> t</ci> <cn type =
'integer'> (-3)</cn> </apply> </vector> </annotation-xml> </semantics>
</math>
z[4]
Content | Presentation | Both
<math> <semantics> <mrow> <mrow> <mo> -</mo> <mn> 10</mn> <mo> + </mo>
</mrow> <msup> <mrow> <mi> X</mi> </mrow> <mrow> <mn> 2</mn> </mrow> </
msup> <mrow> <mo> + </mo> </mrow> <msup> <mrow> <mi> Y</mi> </mrow>
<mrow> <mn> 2</mn> </mrow> </msup> </mrow> <annotation-xml
encoding='MathML-Content'> <apply> <plus/> <cn type = 'integer'> (-10)
</cn> <apply> <power/> <ci variable-value = "0"> X</ci> <cn type =
'integer'> 2</cn> </apply> <apply> <power/> <ci variable-value = "0">
Y</ci> <cn type = 'integer'> 2</cn> </apply> </apply> </annotation-
xml> </semantics> </math>
z[5]
Content | Presentation | Both
<math> <semantics> <mrow> <mn> 10</mn> <mo> ·</mo> <mi> π</mi> </mrow>
<annotation-xml encoding='MathML-Content'> <apply> <times/> <cn type =
'constant'> π</cn> <cn type = 'integer'> 10</cn> </apply> </annotation-
xml> </semantics> </math>
z[6]
Content | Presentation | Both
<math> <semantics> <mrow> <mrow> <mn> 2</mn> <mo> ·</mo> </mrow>
<msqrt> <mrow> <mn> 2</mn> </mrow> </msqrt> <mrow> <mo> ·</mo> </mrow>
<msqrt> <mrow> <mn> 5</mn> </mrow> </msqrt> <mrow> <mo> ·</mo> <mi> π</
mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply>
<times/> <cn type = 'constant'> π</cn> <apply> <root/> <cn type =
'integer'> 5</cn> </apply> <apply> <root/> <cn type = 'integer'> 2</
cn> </apply> <cn type = 'integer'> 2</cn> </apply> </annotation-xml> </
semantics> </math>
z[7]
Content | Presentation | Both
<math> <semantics> <mrow> <mn> 3.162278</mn> </mrow> <annotation-xml
encoding='MathML-Content'> <cn type = 'real'> 3.162278</cn> </
annotation-xml> </semantics> </math>
z[8]
Content | Presentation | Both
<math> <semantics> <mrow> <msqrt> <mrow> <mn> 2</mn> </mrow> </msqrt>
<mrow> <mo> ·</mo> </mrow> <mfenced open = '|' close = '|'> <mrow>
<mrow> <mn> 2</mn> <mo> -</mo> </mrow> <msqrt> <mrow> <mn> 5</mn> </
mrow> </msqrt> </mrow> </mfenced> </mrow> <annotation-xml
encoding='MathML-Content'> <apply> <times/> <apply> <abs/> <apply>
<plus/> <cn type = 'integer'> 2</cn> <apply> <times/> <apply> <root/>
<cn type = 'integer'> 5</cn> </apply> <cn type = 'integer'> (-1)</cn>
</apply> </apply> </apply> <apply> <root/> <cn type = 'integer'> 2</
cn> </apply> </apply> </annotation-xml> </semantics> </math>
z[9]
Content | Presentation | Both
<math> <semantics> <mrow> <mn> 0.3338505</mn> </mrow> <annotation-xml
encoding='MathML-Content'> <cn type = 'real'> 0.3338505</cn> </
annotation-xml> </semantics> </math>
<math><semantics><mrow><mn>0</mn></mrow><annotation-xml
encoding='MathML-Content'><cn type = 'integer'>0</cn></annotation-
xml></semantics></math>

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