I was trying to solve the QHO and I found a power series expansion for the each energy eigenstate ( in the position basis ).
12.
The above result can be derived by power series expansion of \ langle m | H ( x ^ \ mu ) | n \ rangle.
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This is because the germ records the function's power series expansion, and all analytic functions are by definition equal to their power series.
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The Gamma function has a well defined power series expansions at each point of the positive real numbers ( it has a simple pole at zero ).
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Holonomic functions are precisely the generating functions of holonomic sequences : if f ( x ) is holonomic, then the coefficients c _ n in the power series expansion
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The group delay characteristic for this expression can be derived as a power series expansion in ? about zero frequency ( i . e . a MacLaurin series ).
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I answered essential, which is right, but my reasoning was that \ sin ( z ) has a power series expansion with an infinite number of terms of positive degree.
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In mathematics, the "'Lagrange reversion theorem "'gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions.
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They satisfy a linear differential equation with polynomial coefficients, and the coefficients of their power series expansion lie in a fixed algebraic number field and have heights of at most exponential growth.
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Note that the proper powers of intA have rank 3; in the power series expansion of the matrix exponential, the terms X k / k ! for k in the range 50 to 100 dominate the scene.
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