My last blog only managed 250 entries in four years. Let's see how well this one does.
In mathematics, a nonelementary solution is an antiderivative (or indefinite integral) of a given elementary function that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field operations).
Examples of elementary functions with non-elementary solutions include:
1/ln x
e-x2
ex2
(sin x)/x
(cos x)/x
To find antiderivatives of these functions, mathematicians have had to create new functions. For example:
∫ 1/ln x dx = li x (the logarithm integral of x)
∫ e-x2 dx = √π/2 erf x (the error function of x)
∫ ex2 dx = √π/2 erfi x (the imaginary error function of x)
∫ (sin x)/x dx = Si(x) (the sine intergral of x)
∫ (cos x)/x dx = Ci(x) (the cosine intergral of x)
I made an apple pie with cloves when I was in highschool... too many cloves.
Tonight I'm cooking up some pork with herb de provence, extra lavender and brown sugar. When it's done I'll take 2 of the 6 pieces and slice thin and put back in the jus. That should take awhile. Fortunately I'm not too hungry.
Rooms... I need to liberate a chair so I just don't sit on the edge of my bed, like now.
Great choices. Sweet Caroline is actually quite hard to do as karaoke though, I've found. And like you, I find the private karaoke rooms are genius for those of us who can't sing!
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