The description of Bessel_K functions in the Sage Cookbook is
confusing about the order of the arguments.
http://sagemath.org/doc/html/const/node96.html
Here's what it says:
>Here's an example using SAGE's interface to pari's special functions.
>sage: pari('2+I').besselk(3)
>0.04559077184075505871203211094 + 0.02891929465820812820828883526*I #
>32-bit
>0.045590771840755058712032110938791854704 +
>0.028919294658208128208288835257608789842*I # 64-bit
>sage: pari('2').besselk(3) # random
>0.061510458471742038
>The last command can also be executed using the SAGE command
>sage: bessel_K(3,2)
>0.647385390948634
>sage: bessel_K(3,2,100)
>0.64738539094863415315923557097
But in fact the answer 0.061510458471742038 is correct, not random:
sage: bessel_K(2,3)
0.0615104584717420
sage: bessel_K(2,3,100)
0.061510458471742037656820071453
I believe the confusion resulted because in earlier versions of Sage
the order of arguments to
bessel_K was backwards. For instance in Sage 2.8.5:
sage: bessel_K(2,3)
0.647385390948634 # WRONG!!!
Cheers,
Peter
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