# How to write code for replacing result in integral

I have about 100 integral term, the general form of them is as follows:

$$\int \int dx~dy~N_\mu(x)~N_\nu(x)~F(x,y)~A_\nu(y)$$

For each $\mu$ and $\nu$, the definition of functions are different. I have a definite answer for each $\mu$ and $\nu$ for $\int dx~N_\mu(x)~N_\nu(x)~F(x,y)$, (for instance $\int dx~N_1(x)~N_\nu(x)~F(x,y)=term10[1, 0]$) and I've put them all on the list.

term10[1, 0] := 25*pi*(1. + 543*y + 12^y^3)
term11[1, 1] := -208*(3*y + 3)

termList =
List[term10[1, 0], term11[1, 1], term12[1, 2], term13[1, 3],
term14[1, 4], term15[1, 5], term16[1, 6], term17[1, 7],
term18[1, 8], term19[1, 9], term20[2, 0], term21[2, 1],
term22[2, 2], term23[2, 3], term24[2, 4], term25[2, 5],
term26[2, 6], term27[2, 7], term28[2, 8], term29[2, 9],
term30[3, 0], term31[3, 1], term32[3, 2], term33[3, 3],
term34[3, 4], term35[3, 5], term36[3, 6], term37[3, 7],
term38[3, 8], term39[3, 9], term40[4, 0], term41[4, 1],
term42[4, 2], term43[4, 3], term44[4, 4], term45[4, 5],
term46[4, 6], term47[4, 7], term48[4, 8], term49[4, 9],
term50[5, 0], term51[5, 1], term52[5, 2], term53[5, 3],
term54[5, 4], term55[5, 5], term56[5, 6], term57[5, 7],
term58[5, 8], term59[5, 9], term60[6, 0], term61[6, 1],
term62[6, 2], term63[6, 3], term64[6, 4], term65[6, 5],
term66[6, 6], term67[6, 7], term68[6, 8], term69[6, 9],
term70[7, 0], term71[7, 1], term72[7, 2], term73[7, 3],
term74[7, 4], term75[7, 5], term76[7, 6], term77[7, 7],
term78[7, 8], term10[7, 9], term80[8, 0], term81[8, 1],
term82[8, 2], term83[8, 3], term84[8, 4], term85[8, 5],
term86[8, 6], term87[8, 7], term10[8, 8], term89[8, 9],
term90[9, 0], term91[9, 1], term92[9, 2], term93[9, 3],
term94[9, 4], term95[9, 5], term96[9, 6], term10[9, 7],
term98[9, 8], term10[9, 9]]

bet*gGgG*meta^2*
Integrate[N[0]*N[0]*F[x, y]*A[0, y], {x, 0, 1}, {y, 0, 1}]/(188*Pi^2) +
bet*gGgG^3*meta^2*Integrate[N[0]*N[1]*F[x, y]*A[0, y], {x, 0, 1}, {y, 0,
1}]/(75*Pi^4) +
bet^2*gGgG*meta^2*
Integrate[N[0]*N[2]*F[x, y]*A[0, y], {x, 0, 1}, {y, 0, 1}]/(1843*Pi^4) +
jet*meta^2*
Integrate[N[0]*N[3]*F[x, y]*A[0, y], {x, 0, 1}, {y, 0, 1}]/(564*Pi^3)
cc*gGgG^5*meta^2*
Integrate[N[1]*N[1]*F[x, y]*A[1, y], {x, 0, 1}, {y, 0, 1}]/(75*Pi^4) +
fpar*gGgG*meta^2*
Integrate[N[1]*N[2]*F[x, y]*A[1, y], {x, 0, 1}, {y, 0, 1}]/(564*Pi^3) +
mcc*gGgG*meta^2*
Integrate[N[1]*N[3]*F[x, y]*A[1, y], {x, 0, 1}, {y, 0, 1}]/(788*Pi^4) +
mcc*gGgG^3*meta^2*
Integrate[N[2]*N[2]*F[x, y]*A[2, y], {x, 0, 1}, {y, 0, 1}]/(75*Pi^4)+
dd*gGgG*meta^2*
Integrate[N[2]*N[1]*F[x, y]*A[2, y], {x, 0, 1}, {y, 0, 1}]/(564*Pi^3) +...


So I need a code to replace results term mu nu[mu, nu] into integrals, for calculating the next integral. maybe TransformationFunctions can help, but I don't know how use it.

• term[mu_Integer, nu_Integer[ := Integrate[<integrand code>, x, y]? – Michael E2 Aug 8 '18 at 17:41
• @MichaelE2 term[mu_Integer, nu_Integer] :=... – rhermans Aug 8 '18 at 17:42
• @rhermans Thanks. Might also be that the integration should be Integrate[term10[mu, nu] A[nu, y], y]. After helping thousands of folks on this site, with descriptions of code of varying clarity and accuracy, I feel there's no better substitute for complete working code. – Michael E2 Aug 8 '18 at 17:53
• @MichaelE2 as I said I have 100 term, I should replace each integral with $term\mu\nu[\mu, \nu]$ for 100 term. My problem is that I don't wanted replace $term\mu\nu[\mu, \nu]$ with $\int dx~N_\mu(x)~N_\nu(x)~F(x,y)$, manually – asal Aug 8 '18 at 19:05
• That's why I wrote a general rule to replace all of them with one line of code. Now, you have 'term10[0, 0] in your question, but your comment suggests that it should have been term00[0, 0]`. Is that so? If yes, then I was mislead. If you gave them all different names $term\mu\nu$, then that will prove somewhat inconvenient. As I said, complete code is the best way to get good help with problems. A minimal working example (MWE) is what the community generally prefers, esp. if you code is very long. – Michael E2 Aug 8 '18 at 20:15