User:Dhatfield/sandbox

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$cps\left(E,N,{\mbox{Rw}},k,t_{0},C,{\mbox{fps}}\right)\ =\ {\frac {\mbox{fps}}{{\left({\mbox{fps}}-1\right)}{\left({\frac {\mbox{fps}}{{\mbox{fps}}-1}}+{\frac {\mbox{Rw}}{{\left(-{\frac {{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E}{{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1}}+1\right)}^{N}e^{\left(-\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{C}k\right)}-1}}\right)}}}$

${\frac {dcps}{dRw}}\left(E,N,{\mbox{Rw}},k,t_{0},C,{\mbox{fps}}\right)\ =\ {\frac {{\left({\frac {{\left(-{\frac {0.5\,{\left(-{\frac {{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E}{{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1}}+1\right)}^{N}Ckt_{0}\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{\left(C-1\right)}e^{\left(-\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{C}k\right)}}{{\left(-0.5\,{\mbox{Rw}}+1\right)}^{2}}}-{\left({\frac {{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E{\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}-1\right)}}{{\left({\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1\right)}^{2}N}}-{\frac {E{\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}-1\right)}}{{\left({\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1\right)}N}}\right)}N{\left(-{\frac {{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E}{{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1}}+1\right)}^{\left(N-1\right)}e^{\left(-\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{C}k\right)}\right)}{\mbox{Rw}}}{{\left({\left(-{\frac {{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E}{{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1}}+1\right)}^{N}e^{\left(-\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{C}k\right)}-1\right)}^{2}}}-{\frac {1}{{\left(-{\frac {{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E}{{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1}}+1\right)}^{N}e^{\left(-\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{C}k\right)}-1}}\right)}{\mbox{fps}}}{{\left({\mbox{fps}}-1\right)}{\left({\frac {\mbox{fps}}{{\mbox{fps}}-1}}+{\frac {\mbox{Rw}}{{\left(-{\frac {{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}E}{{\left(E-1\right)}{\left({\left(-{\mbox{Rw}}+1\right)}^{\left({\frac {1}{N}}\right)}-1\right)}-1}}+1\right)}^{N}e^{\left(-\left({\frac {t_{0}}{-0.5\,{\mbox{Rw}}+1}}\right)^{C}k\right)}-1}}\right)}^{2}}}$

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: MathJax internal buffer size exceeded; is there a recursive macro call?"): {\displaystyle \left(E,a,b\right)\ {\mapsto }\ \left(R_{w_{c}}={\frac {{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(-R_{w_{c}}+1\right)}^{N}a\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\left({\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{N}-E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-a\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}+{\sqrt {-{\left({\left(ab-a\right)}E^{2}-{\left(a^{2}+ab-a\right)}E\right)}{\left(-R_{w_{c}}+1\right)}^{\left(2\,N\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-2\right)}+{\left(2\,{\left({\left(ab-a\right)}E^{2}-{\left(a^{2}+ab-a\right)}E\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-2\right)}-{\left({\left(a+2\,b-2\right)}E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(a+b-1\right)}E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}\right)}{\left(-R_{w_{c}}+1\right)}^{N}-{\left({\left(ab-a\right)}E^{2}-{\left(a^{2}+ab-a\right)}E\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-2\right)}+{\left({\left(b-1\right)}E^{3}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\left({\left(b-1\right)}E^{3}-{\left(a+2\,b-2\right)}E^{2}+{\left(a+b-1\right)}E\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-1\right)}\right)}{\left(-R_{w_{c}}+1\right)}^{\left(2\,N-1\right)}+{\left({\left(b-1\right)}E^{3}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(a+2\,b-2\right)}E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(a+b-1\right)}E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-1\right)}-{\left({\left(b-1\right)}E^{3}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(a+2\,b-2\right)}E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(a+b-1\right)}E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}}}}{{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(Ea-a\right)}{\left(-R_{w_{c}}+1\right)}^{N}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}+E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(Ea-a\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\left({\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-2\,E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{N}-2\,E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}}},\,R_{w_{c}}={\frac {{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(-R_{w_{c}}+1\right)}^{N}a\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\left({\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{N}-E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-a\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\sqrt {-{\left({\left(ab-a\right)}E^{2}-{\left(a^{2}+ab-a\right)}E\right)}{\left(-R_{w_{c}}+1\right)}^{\left(2\,N\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-2\right)}+{\left(2\,{\left({\left(ab-a\right)}E^{2}-{\left(a^{2}+ab-a\right)}E\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-2\right)}-{\left({\left(a+2\,b-2\right)}E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(a+b-1\right)}E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}\right)}{\left(-R_{w_{c}}+1\right)}^{N}-{\left({\left(ab-a\right)}E^{2}-{\left(a^{2}+ab-a\right)}E\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-2\right)}+{\left({\left(b-1\right)}E^{3}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\left({\left(b-1\right)}E^{3}-{\left(a+2\,b-2\right)}E^{2}+{\left(a+b-1\right)}E\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-1\right)}\right)}{\left(-R_{w_{c}}+1\right)}^{\left(2\,N-1\right)}+{\left({\left(b-1\right)}E^{3}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(a+2\,b-2\right)}E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(a+b-1\right)}E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(2\,N-1\right)}-{\left({\left(b-1\right)}E^{3}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(a+2\,b-2\right)}E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(a+b-1\right)}E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}}}}{{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-{\left(Ea-a\right)}{\left(-R_{w_{c}}+1\right)}^{N}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}+E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+{\left(Ea-a\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{\left(N-1\right)}-{\left({\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}+E^{2}{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}-2\,E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}\right)}\left({\frac {R_{w_{c}}^{2}a-{\left(a-b+1\right)}R_{w_{c}}-b+1}{ER_{w_{c}}-R_{w_{c}}+1}}\right)^{N}-2\,E{\left(-R_{w_{c}}+1\right)}^{\left(N-1\right)}}}\right)}