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Though the two are supposed to be identical when their first argument is an integer, they begin to diverge from one another as their second argument increases in magnitude, demonstrated here with first argument zero though I tested with first argument of one as well and observed similar behavior:
besselj(0, 1) gives 0.7651976865579666
angerj(0,1) gives 0.7651976865579666
besselj(0, 10) gives -0.2459357644513912
angerj(0,10) gives -0.2459357644513481
besselj(0, 100) gives 0.01998585030422332
angerj(0,100) gives -0.04425859855968436
besselj(0, 1000) gives 0.024786686152420027
angerj(0,1000) gives 0.08136533156802234
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