- #1
wil3
- 179
- 1
I have tried mathematica, and it says it lacks the means to solve it:
The function
[tex]
g6_{\mu,\sigma}[x]
[/tex]
represents the SIXTH derivative of a normal distribution with unspecified parameters. I am looking to solve the relation:
[tex]
g6_{\mu,\sigma}[\mu+ \frac{\delta}{2}] + g6_{\mu,\sigma}[\mu - \frac{\delta}{2}] = 0
[/tex]
in terms of [tex]\delta[/tex]. I have a feeling that the answer does not depend on mu, just sigma.
The application is finding the minimum separation required between the central peaks of two 4-derivative gaussian curves such that there occur no inflections on the consolidated central peak. This is related to Sparrow's criterion.
Thank you very much for any help.
The function
[tex]
g6_{\mu,\sigma}[x]
[/tex]
represents the SIXTH derivative of a normal distribution with unspecified parameters. I am looking to solve the relation:
[tex]
g6_{\mu,\sigma}[\mu+ \frac{\delta}{2}] + g6_{\mu,\sigma}[\mu - \frac{\delta}{2}] = 0
[/tex]
in terms of [tex]\delta[/tex]. I have a feeling that the answer does not depend on mu, just sigma.
The application is finding the minimum separation required between the central peaks of two 4-derivative gaussian curves such that there occur no inflections on the consolidated central peak. This is related to Sparrow's criterion.
Thank you very much for any help.