(adsbygoogle = window.adsbygoogle || []).push({}); Analytical form of an "Interpolated" function

Hallo,

I have a question on the use of "Interpolation" function in Mathematica.

I am wondering whether it is possible to extract an analytical expression

for a function built using the "Interpolation" option. Say, I have the following

function of two variable f(x,y) represented on a grid:

Ra=Interpolation[{

{{ 2.777897, 0.000000}, -0.202683},

{{ 2.777897, 0.043633}, -0.203579},

{{ 2.777897, 0.087266}, -0.200988},

{{ 2.777897, 0.130900}, -0.192908},

{{ 2.777897, 0.174533}, -0.176695},

{{ 2.777897, 0.218166}, -0.155857},

{{ 2.777897, 0.261799}, -0.129889},

{{ 2.815692, 0.000000}, -0.202618},

{{ 2.815692, 0.043633}, -0.203585},

{{ 2.815692, 0.087266}, -0.201401},

{{ 2.815692, 0.130900}, -0.194172},

{{ 2.815692, 0.174533}, -0.179481},

{{ 2.815692, 0.218166}, -0.163498},

{{ 2.815692, 0.261799}, -0.140403},

{{ 2.853486, 0.000000}, -0.201962},

{{ 2.853486, 0.043633}, -0.203003},

{{ 2.853486, 0.087266}, -0.201219},

{{ 2.853486, 0.130900}, -0.194830},

{{ 2.853486, 0.174533}, -0.181844},

{{ 2.853486, 0.218166}, -0.170511},

{{ 2.853486, 0.261799}, -0.150171},

{{ 2.891281, 0.000000}, -0.200745},

{{ 2.891281, 0.043633}, -0.201863},

{{ 2.891281, 0.087266}, -0.200472},

{{ 2.891281, 0.130900}, -0.194926},

{{ 2.891281, 0.174533}, -0.184095},

{{ 2.891281, 0.218166}, -0.176901},

{{ 2.891281, 0.261799}, -0.159191},

{{ 2.929075, 0.000000}, -0.198999},

{{ 2.929075, 0.043633}, -0.200197},

{{ 2.929075, 0.087266}, -0.199196},

{{ 2.929075, 0.130900}, -0.194513},

{{ 2.929075, 0.174533}, -0.186552},

{{ 2.929075, 0.218166}, -0.182673},

{{ 2.929075, 0.261799}, -0.167464},

{{ 2.966870, 0.000000}, -0.196757},

{{ 2.966870, 0.043633}, -0.198037},

{{ 2.966870, 0.087266}, -0.197426},

{{ 2.966870, 0.130900}, -0.193666},

{{ 2.966870, 0.174533}, -0.189150},

{{ 2.966870, 0.218166}, -0.187834},

{{ 2.966870, 0.261799}, -0.174997},

{{ 3.004664, 0.000000}, -0.194050},

{{ 3.004664, 0.043633}, -0.195418},

{{ 3.004664, 0.087266}, -0.195205},

{{ 3.004664, 0.130900}, -0.192492},

{{ 3.004664, 0.174533}, -0.191623},

{{ 3.004664, 0.218166}, -0.192395},

{{ 3.004664, 0.261799}, -0.181796},

{{ 3.042459, 0.000000}, -0.190913},

{{ 3.042459, 0.043633}, -0.192374},

{{ 3.042459, 0.087266}, -0.192580},

{{ 3.042459, 0.130900}, -0.191144},

{{ 3.042459, 0.174533}, -0.193806},

{{ 3.042459, 0.218166}, -0.196366},

{{ 3.042459, 0.261799}, -0.187872},

{{ 3.080253, 0.000000}, -0.187381},

{{ 3.080253, 0.043633}, -0.188943},

{{ 3.080253, 0.087266}, -0.189609},

{{ 3.080253, 0.130900}, -0.189813},

{{ 3.080253, 0.174533}, -0.195628},

{{ 3.080253, 0.218166}, -0.199759},

{{ 3.080253, 0.261799}, -0.193240},

{{ 3.118048, 0.000000}, -0.183492},

{{ 3.118048, 0.043633}, -0.185166},

{{ 3.118048, 0.087266}, -0.186363},

{{ 3.118048, 0.130900}, -0.188646},

{{ 3.118048, 0.174533}, -0.197061},

{{ 3.118048, 0.218166}, -0.202589},

{{ 3.118048, 0.261799}, -0.197915},

{{ 3.155842, 0.000000}, -0.179285},

{{ 3.155842, 0.043633}, -0.181090},

{{ 3.155842, 0.087266}, -0.182933},

{{ 3.155842, 0.130900}, -0.187658},

{{ 3.155842, 0.174533}, -0.198096},

{{ 3.155842, 0.218166}, -0.204871},

{{ 3.155842, 0.261799}, -0.201916},

{{ 3.193637, 0.000000}, -0.174801},

{{ 3.193637, 0.043633}, -0.176764},

{{ 3.193637, 0.087266}, -0.179435},

{{ 3.193637, 0.130900}, -0.186750},

{{ 3.193637, 0.174533}, -0.198733},

{{ 3.193637, 0.218166}, -0.206622},

{{ 3.193637, 0.261799}, -0.205261}

}]

Mathematica makes an "Interpolated" function by a polynomial of 3rd or 4th oder out of this.

The question is if there is an elegant option to extract the coefficients of this polynomial

(besides that of taking the 1st, 2nd, etc derivatives of the function, which is quite tedious).

Many thanks!

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# Analytical form of an Interpolated function

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