[Jprogramming] Derivatives of o. family

[Roger Hui]

Thanks.

John Randall, being a professor of mathematics, would have
a much easier time providing that table than it would be
for you and me.



----- Original Message -----
From: Dan Bron <j at bron.us>
Date: Saturday, February 19, 2011 10:26
Subject: Re: [Jprogramming] Derivatives of o. family
To: 'Programming forum' <programming at jsoftware.com>

> Roger wrote:
> >  If you can suggest the desired derivates/integrals, 
> >  it would greatly aid in filling the gaps. e.g.
> >
> >            derivative      integral
> >  0&o.
> >  4&0.
> 
> Having long since forgotten my undergraduate calculus courses, I 
> googled for
> "online derivative calculator" and found this:
> 
> 	http://www.numberempire.com/derivatives.php
> 	http://www.numberempire.com/integralcalculator.php
>   
> Looking up the definitions of 0&o. and 4&o. (viz, -.&.:*: and >:&.:*:
> respectively), and plugging them into the above, I came up with:
> 
> 	f      f d. 
> 1               f d. _1                      
> 	0&o.   -@:(% -. *&:%: >:)   -:@:(_1&o. + ] 
> * -. *&:%: >:)
> 	4&o.   % 
> >:&.:*:            -:@:(_5&o. + ] * >:&.:*:)    
> 
> Verification left as an exercise for those who haven't forgotten their
> undergraduate calculus courses :)  
> 
> -Dan
> 
> PS:  Of course we have some leeway with J style (e.g. we 
> could write them
> all paren free by replacing the @ parts with NVV equivalents, 0 -
> ... and 2
> %~ ... etc).