The zero point need not be the center of a power series. If they are centered at any point x is a, the series will have powers of (xa) rather than powers of x.
Is 0 the center of all power series?
- The zero point need not be the center of a power series. If they are centered at any point x=a, the series will have powers of (xa) rather than powers of x.
- Assume that the differential equation has a solution with the formula y(x)=n=0anxn.
- Differentiate the power series term by term to obtain y′(x)=n=1nanxn1.
- The differential equation should be changed to reflect the power series expressions.
- Moreover, the constant 0, which is the y-intercept in the equation y=0, is present. The constant 0, which stands in for the x-intercept in the equation x=0. As a result, the graph of a vertical, straight line that passes through the origin can be used to illustrate the equation x=0.
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