Science Quiz / Mathematical Functions (difficult!)

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Can you name the mathematical functions?

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HintFunction
Function of form f(x)=Ax^2 + Bx + C
Function of form f(x)=ln(x)
Function of form f(x)=1/csc(x)
Function of form f(x)=x!
Extension of above function to complex domain
Logarithmic derivative of above function
Solutions to certain differential equation and used in studying electromagnetism; also known as cylinder function
Function that analytically continues f(x)=[Sum from n=1 to infinity of 1/n^x] to the complex domain
Function f(x) defined as f(x)=0 for all x except for when f(x) is infinitely large at x=0 such that the total integral is 1
Function f(x) defined as f(x)=0 for negative x and f(x)=1 for positive x. Integral of above function.
Function that maps quadratic irrationals to rational numbers and rational numbers to dyadic rationals on the unit interval. First defined by a German, and has a symbol in its name.
Function defined as f(x)=[Sum from n=0 to infinity of (A^n)*cos(B*n*Pi*x)] with A between 0 and 1 and B a positive odd integer. Function shows fractal behaviour.

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