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Understanding Recursive Functions in Polynomial Growth

This explanation delves into the mechanics of recursive functions and polynomials, showcasing how specific values are derived through a systematic breakdown. Starting with initial conditions, the function demonstrates how outputs depend on previous inputs, resulting in various polynomial growth patterns. By analyzing the recursive relationships, we can comprehend the functional dependencies and their significance in mathematical modeling. The process illustrates dynamic changes in value outputs based on the interplay of coefficients and recursive structures.

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Understanding Recursive Functions in Polynomial Growth

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Presentation Transcript

  1. m=0;n=0

  2. m<1;n=0 m=0;n<1

  3. y(1,1)=-1*1=-1 m=1;n=1

  4. y(2,1)=-2*1+-1*2=-4 m=2;n=1

  5. y(3,1)=-2*2=-4 m=3;n=1

  6. y(1,2)=-1*3+0*1=-3 m=1;n=2

  7. y(2,2)=-2*3+-1*4+3*1+0*2=-7 m=2;n=2

  8. y(3,2)=-2*4+3*2=-2 m=3;n=2

  9. y(1,3)=0*3=0 m=1;n=3

  10. y(2,3)=3*3+0*4=9 m=2;n=3

  11. y(3,3)=3*4=12 m=3;n=3

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