Order approximation for rational polynomialI have this fraction: ( − 12 a 3 ) d 3 + ( 4 w a 3 − 16 a 2 ) d 2 + ( 5 w a 2 − 8 a ) d − a 2 w 2 + 2 a w − 1 ( − 12 w a 4 + 12 a 3 ) d 3 + ( 4 a 4 w 2 − 20 a 3 w + 16 a 2 ) d 2 + ( 4 a 3 w 2 − 11 a 2 w + 7 a ) d + a 2 w 2 − 2 a w + 1 How can I approximate it so it may be written as a function of increasing order of d? As in f ( d ) + f ( d 2 ) + H . O . TI have tried using Taylor series but that is centered around a point (which I don't want). I am looking into Pade approximation but am utterly confused. Can someone help me?

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Order approximation for rational polynomialI have this fraction:             (      −      12              a        3            )              d        3            +      (      4      w              a        3            −      16              a        2            )              d        2            +      (      5      w              a        2            −      8      a      )      d      −              a        2                    w        2            +      2      a      w      −      1              (      −      12      w              a        4            +      12              a        3            )              d        3            +      (      4              a        4                    w        2            −      20              a        3            w      +      16              a        2            )              d        2            +      (      4              a        3                    w        2            −      11              a        2            w      +      7      a      )      d      +              a        2                    w        2            −      2      a      w      +      1      How can I approximate it so it may be written as a function of increasing order of d? As in   f  (  d  )  +  f  (      d    2    )  +  H  .  O  .  TI have tried using Taylor series but that is centered around a point (which I don&#039;t want). I am looking into Pade approximation but am utterly confused. Can someone help me?

Ordettyreomqu · Accepted Answer

This problem is                    n        1                    d        3            +              n        2                    d        2            +              n        3            d      +              n        4                            n        5                    d        3            +              n        6                    d        2            +              n        7            d      +              n        8            for complicated values of the constants       n    1    ,  …  ,      n    8  Big O notation is useful in two contexts here; either for   d  →  0 or for   d  →  ∞If you expand as   d  →  0, you get            n      4              n      8        +  d                    n        3                    n        8            −              n        7                    n        4                    n      8      2        +  O  (      d    2    )If you expand as   d  →  ∞ , you get            n      1              n      5        +      1    d                      n        2                    n        5            −              n        6                    n        1                    n      5      2        +  O      (          1              d        2              )  You can calculate these easily (and more terms if desired) on alpha.

Order approximation for rational polynomial I have this fraction: ( &#x221

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