# How to do Interpolation to this function after given b this values

Mathematica Asked by user69941 on August 29, 2020

  [Chi][b_] := (Z/k)*NIntegrate[Subscript[f, pp1][q]*Subscript[F, pp1][q]*BesselJ[0, q*b]*q, {q, 0, b}];


bList = Table[b, {b, 0, 5.1 , 0.05}]

where:
Z = 6;
k=1.55246;

 Subscript[f, pp1][q_]=(6.254736279890945*(1 - 1.4511668475476842))/E^(0.2115*q^2)

Subscript[F, pp1][q_] := ((4*Pi)/q)*NIntegrate[Subscript[[Rho], p][r]*Sin[q*r]*r, {r, 0, Infinity}];

Subscript[[Rho], p][r_]=0.013132593248303927/(1 + (E^(1.7543859649122808*(-2.380427976610103 - r)) + E^(1.7543859649122808*(-2.380427976610103 + r)))*
(0.5 + 0.08823886490842314*r^2)^1.5)


Clear["Global*"]

Subscript[f, pp1][q_] = (6.254736279890945*(1 - 1.4511668475476842))/
E^(0.2115*q^2);

Subscript[F, pp1][q_?NumericQ] := ((4*Pi)/q)*
NIntegrate[Subscript[ρ, p][r]*Sin[q*r]*r, {r, 0, Infinity}];

Subscript[ρ, p][r_] =
0.013132593248303927/(1 +
(E^(1.7543859649122808*(-2.380427976610103 - r)) +
E^(1.7543859649122808*(-2.380427976610103 + r)))*(0.5 +
0.08823886490842314*r^2)^1.5);

χ[b_?NumericQ] := (Z/k)*NIntegrate[
Subscript[f, pp1][q]*Subscript[F, pp1][q]*BesselJ[0, q*b]*q, {q, 0, b}];

Z = 6; k = 1.55246;

data = {#, χ[#]} & /@ Range[0, 5.1, 0.05] // Quiet;

f = Interpolation[data];

Plot[f[b], {b, 0, 5.1},
Epilog -> {Red, AbsolutePointSize[3], Point[data]}]
`

Answered by Bob Hanlon on August 29, 2020