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Entire Functions Classification
30
Flashcards
0/30
f(z) = sin(z)
Order 1, Type 1
f(z) = e^{az} (a \\in \\mathbb{C}, a \\neq 0)
Order 1, Type 1
f(z) = \\sum_{n=0}^{\\infty} z^{2^n}
Order \\infty, Type 2
f(z) = cos(z)
Order 1, Type 1
f(z) = sinh(z)
Order 1, Type 1
f(z) = \\sin(z) + \\sinh(z)
Order 1, Type 1
f(z) = e^{z^2}
Order 2, Type 2
f(z) = \\exp(z + z^{-1})
Order 1, Type 2
f(z) = z^n (n > 0)
Order n, Type 1
f(z) = \\exp(-z^n) (n>1)
Order frac{1}{n}, Type 1
f(z) = \\exp(-e^z)
Order \\infty, Type 3
f(z) = \\sin(\\sqrt{z})
Order frac{1}{2}, Type 1
f(z) = \\Gamma(z)
Infinite Order
f(z) = \mathrm{Ai}(z)
Order frac{3}{2}, Type 2
f(z) = e^z
Order 1, Type 1
f(z) = e^{z^a} (a > 1, a otin \\mathbb{Z})
Order frac{1}{a}, Type 2
f(z) = e^{e^z}
Infinite Order
f(z) = \\log(z)
Undefined
f(z) = \\cos(z^2)
Order 1, Type 2
f(z) = \\cos^{-1}(z)
Undefined
f(z) = \mathrm{Bi}(z)
Order frac{3}{2}, Type 2
f(z) = e^{-z^2}
Order frac{1}{2}, Type 2
f(z) = \\sum_{n=0}^{\\infty} \\frac{z^n}{n!}
Order 1, Type 1
f(z) = \\sum_{n=0}^{\\infty} \\frac{z^n}{n^n}
Order 0, Type 2
f(z) = \\zeta(z)
Undefined
f(z) = z!
Infinite Order
f(z) = z^{1/n} (n>0)
Order frac{1}{n}, Type 1
f(z) = \\tan(z)
Order 1, Type 1
f(z) = \\exp(\\cos(z))
Order 1, Type 1
f(z) = (1 + z/n)^n
Order 1, Type 1
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