Treat a polynomial in as a polynomial in with hidden coefficients depending on .
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Create another sequence using different labels. Note that the table of last used indices is keyed by the label name (in this case C).
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C(1) = 10 * x - 98 * z + 23
C(2) = 4 * x ** 2 + 7 * x * z - 10 * z ** 2 + 40 * x + 61 * z + 8
C(3) = 87 * x ** 3 - 83 * x ** 2 * z + 42 * x * z ** 2 - 29 * z **
# 3 - 10 * x ** 2 - 50 * x * z + 95 * z ** 2 + 23 * x + 11 * z - 49
C(4) = 22 * x ** 4 - 56 * x ** 3 * z + 62 * x ** 2 * z ** 2 + 75 *
# x * z ** 3 - 47 * z ** 4 - 82 * x ** 2 * z - 92 * x * z ** 2 + 40
# * z ** 3 + 80 * x ** 2 + 6 * x * z - 81 * z ** 2 + 74 * x + 91 *
#z + 68
C(5) = 7 * x ** 5 + 55 * x ** 4 * z + 62 * x ** 3 * z ** 2 + 44 *
#x ** 2 * z ** 3 - 72 * x * z ** 4 + 10 * z ** 5 + 94 * x ** 4 - 97
# * x ** 3 * z - 71 * x ** 2 * z ** 2 - 37 * x * z ** 3 - 31 * z **
# 4 + 73 * x ** 3 + 17 * x ** 2 * z + 23 * x * z ** 2 + 51 * z ** 3
# + 75 * x ** 2 - 87 * x * z - 77 * z ** 2 - 44 * x - 95 * z - 1
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The following Frobenius series solution to a differential equation has complicated coefficients, which obscure the structure of the solution.
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Example based on content provided in Chapter 2 of Essential Maple 7.