Fear of needles to the phobic imagining the procedure being performed on themselves. Recent neuroscience research shows that feeling a pin prick sensation and watching someone else's hand get pricked by a pin activate the same part of the brain. Fear of needles, especially in its more severe forms, is often comorbid with other phobias and psychological ailments; for example, iatrophobia, or an irrational fear of doctors, is often seen in needle phobic patients. A needle phobic patient does not need to physically be in a doctor's office to experience panic attacks or anxiety brought on by needle phobia. There are many triggers
Proof that π is irrational enough and that the sequence of all "g" converges to 0. But a sequence of numbers greater than or equal to |"y"| cannot converge to 0. Since "f"(/4) = cos(/2) = 0, it follows from claim 3 that /16 is irrational and therefore that is irrational. On the other hand, since another consequence of Claim 3 is that, if "x" ∈ Q \ {0}, then tan "x" is irrational. Laczkovich's proof is really about the hypergeometric function. In fact, "f"("x") = "F"(k; −"x") and Gauss found a continued fraction expansion of the hypergeometric function using its functional equation. This allowed