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s) Say that f(æ) is a nicely-behaved function that has a Taylor series (as all well- as the input to behaved functions do). It is also an odd function of x. Somebody then plugs in q² this function, defining a function g(q) = f(q²). If we try to write down a Taylor series for g, will there be odd powers of q in this Taylor series? Why or why not?

s) Say that f(æ) is a nicely-behaved function that has a Taylor series (as all well- as the input to behaved functions do). It is also an odd function of x. Somebody then plugs in q² this function, defining a function g(q) = f(q²). If we try to write down a Taylor series for g, will there be odd powers of q in this Taylor series? Why or why not?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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s) Say that f(x) is a nicely-behaved function that has a Taylor series (as all well- behaved functions do). It is also an odd function of x. Somebody then plugs in q² as the input to this function, defining a function g(q) = f(q²). If we try to write down a Taylor series for there be odd powers of q in this Taylor series? Why or why not? will
Transcribed Image Text:s) Say that f(x) is a nicely-behaved function that has a Taylor series (as all well- behaved functions do). It is also an odd function of x. Somebody then plugs in q² as the input to this function, defining a function g(q) = f(q²). If we try to write down a Taylor series for there be odd powers of q in this Taylor series? Why or why not? will
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