3 ms·
That's awesome. Glad to see your method worked. If you ever have a chance to encounter a serious mathematician, they can probably give you the proper name of it
by goldenkey 4y ago
That's awesome. Glad to see your method worked. If you ever have a chance to encounter a serious mathematician, they can probably give you the proper name of it. Or perhaps we'll have to name it the Yarg integral :-)
- yarg 4y agoI've just been thinking of it as differentiation via integration. It took me until the end to realise that all I'd done was derive a form for the second derivative of F(x).
- goldenkey 4y agoAh yes, this is why epsilon squared equals 0 in the dual numbers -- to automatically remove all higher order derivatives when they appear. Exponents on derivatives are indicate of their rank/order.
- yarg 4y agoIt's the second symmetric derivative. https://en.wikipedia.org/wiki/Symmetric_derivative#The_second_symmetric_derivative https://en.wikipedia.org/wiki/Symmetric_derivative#The_secon... https://en.wikipedia.org/wiki/Second_derivative#Limit https://en.wikipedia.org/wiki/Second_derivative#Limit > The limit is called the second symmetric derivative. Note that the second symmetric derivative may exist even when the (usual) second derivative does not. > This limit can be viewed as a continuous version of the second difference for sequences. So it actually can do what I intended it to do, nothing original - but there was a degree of satisfaction in deriving it myself.
- goldenkey 4y agoThanks yarg, I just learned something new.