# 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, Point[data]}] Answered by Bob Hanlon on August 29, 2020

## Related Questions

### How conflicting patterns are resolved?

0  Asked on April 11, 2021

### Difference between the infinite rewriting behavior of evaluation and ReplaceRepeated

0  Asked on April 11, 2021 by asd1dsa

### How to show the map of a complex function ( plane z incl the basic square grid to plane w?

1  Asked on April 11, 2021

### Why does Molecule` return a molecule for an incorrect SMILES string?

1  Asked on April 11, 2021 by ljfan

### List X is a starter of List Y

2  Asked on April 11, 2021 by imida-k

### Filing region between plots with ListLinePlot?

2  Asked on April 11, 2021 by campos

### Error propagation code

2  Asked on April 11, 2021 by dinesh-kumar

### Weird looking ListDensityPlot graph

2  Asked on April 11, 2021

### Opposite of “Extend Selection?”

0  Asked on April 11, 2021

### Find equal elements on a list

2  Asked on April 11, 2021 by sigur

### Issue with the Laplacian in Cylindrical Coordinates

2  Asked on April 11, 2021 by siddharth-chaini

### Visualize the optimal point for distribution with three parameters

1  Asked on April 10, 2021 by a-day

### Fail to Export/Import seq2seq model (NER) to MXNet or ONNX

0  Asked on April 10, 2021 by fortsaint

### Numerically solve of a system of PDEs

1  Asked on April 10, 2021

### Placing and styling EdgeLabels in Graph

1  Asked on April 10, 2021

### Finding the coefficients of an expression

2  Asked on April 10, 2021 by mark-r

### Unwanted scaling when overlaying GraphicsComplex graphic onto image?

1  Asked on April 10, 2021 by gnaprs

### Colormaps for linear visual perception AND grayscale printing

5  Asked on April 10, 2021 by dpf

### Controlling plots with sliders without using Manipulate

2  Asked on April 9, 2021 by alel

### Heat balance in layer coupled via BC

2  Asked on April 9, 2021