The even coefficient of odd function is equal to 0, and the odd coefficient of even function is equal to 0,

One variable multiple power function:
f(X)=a(0)+a(1)×X+a(2)×X²+a(3)×X³+…… +a(n)×X^n
1. If f (x) is an odd function, the coefficients a (0), a (2), a (4) It's all zero
2. If f (x) is an even function, the coefficients a (1), a (3), a (5) It's all zero

RELATED INFORMATIONS

1. Is the odd power of odd function odd function or even function, even power? And even function odd power is odd function or even function, even power? For example, (SiNx) ^ n, n are odd and even numbers respectively (cosx) ^ n, n are odd and even numbers respectively
2. Let a be an even function and B be an odd function, then the sum difference product quotient of a and B, the sum difference product quotient of a and a, and the sum difference product quotient of B and B are odd or even functions respectively? Even + - odd =? (even or odd) even × / odd =? (even or odd) Even + - even =? (even or odd) even × / even =? (even or odd) Odd + - odd =? (even or odd) odd × / odd =? (even or odd)
3. Odd function + non odd non even function=_______ Even function + non odd non even function=_______ Non odd non even function + non odd non even function=_______ Non odd non even function × non odd non even function=_______
4. The problem of increasing and decreasing functions and the problem of odd and even functions The definition field of y = f (x) is R. for any a, B belonging to R, f (a + b) = f (a) + F (b). When x > 0, f (x) < 0 holds, f (3) = - 3 1) It is proved that the function is a decreasing function over R 2) Prove that a function is an odd function 3) Functions in [M, n] m, n all belong to the range of n *
5. Observe the following three lines: - 3, 9, - 27, 81, - 243 -5，7，-29，79，-245，… -1，3，-9，27，-81… (1) What is the order of the first row? (2) What is the relationship between the number of the second and third rows and the number of the first row? (3) Take the 10th number of the three rows and calculate the sum of the three numbers
6. English translation
7. What are the common factors of 64 and 45 Yes!
8. Which word is the instrument of measurement or calculation And what's the word "hear" or "hear"
9. Uncle Li's family has 42 chickens, half of which are ducks. How many chickens and ducks do Uncle Li's family raise?
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11. How to judge non odd and non even functions
12. Even function multiplied by non odd non even function is? For example, LNX * cosx Is odd function multiplied by non odd and non even function? For example, LNX * SiNx Does periodic function change periodically after multiplying by aperiodic function? For example, LNX * cosx?
13. What is a non odd non even function multiplied by a non odd non even function
14. It is proved that the monotonicity of the symmetric interval of even function is opposite Ah You know, you know, There are only two things I don't understand. I'm in a hurry Let y = f (x) be an even function, then f (- x) = f (x) If X1 > x2 > 0, then - x1f (x2), that is, f (x) decreases In the same way, it can be proved that f (x) is a decreasing function on the positive half axis and an increasing function on the negative half axis In this case, why is it necessary to assume that the positive semiaxis is monotonically increasing? Finally, why is f (- x1) > F (x2), that is, f (x) decreasing? How to judge?
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18. The sum of the sum, difference and quotient of a fraction added, subtracted and divided by itself is 13 out of 3
19. When a fraction is added, subtracted, and divided with itself, the sum, difference, and quotient of the sum, difference, and quotient are added up to two fifths（
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