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9.4 THE EXPONENTIAL GENERATING FUNCTION

9.5 THE SUMMATION OPERATOR

Discrete Mathematics

NYCU

312706031

Han Cheng

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9.4 THE EXPONENTIAL GENERATING FUNCTION

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SELECTIONS

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ARRANGEMENTS

 

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ORDINARY GF

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EXPONENTIAL GF

 

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EXAMPLE 9.26

  • Q: In how many ways can four of the letters in ENGINE be arranged?

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EXAMPLE 9.28.A

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EXAMPLE 9.28.B

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9.5 THE SUMMATION OPERATOR

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THE SUMMATION OPERATOR

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EXAMPLE 9.30

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Generating Function

Sequence

1/(1-x)

1, 1, 1, …

1/(1-x)2

1, 2, 3, …

x+x2

0, 1, 1, 0, 0, …

(x+x2)/(1-x)

0, 1, 2, 2, 2, …

(x+x2)/(1-x)2

0, 1, 3, 5, 7, …

(x+x2)/(1-x)3

0, 1, 4, 9, 16, …

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GENERATING FUNCTION

CALCULATOR

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LIMITATIONS

  • This program cannot count Maclaurin series nor the summation operator
    • Cause they all have infinite sequence members

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