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"# LegendreAssoc\n",
"Example describing the usage of different kinds of Associate Legendre Polynomials.\n",
"\n",
"To execute the macro type in:\n",
"\n",
"```cpp\n",
"root[0] .x LegendreAssoc.C\n",
"```\n",
"\n",
"It draws common graphs for first 5\n",
"Associate Legendre Polynomials\n",
"and Spherical Associate Legendre Polynomials.\n",
"Their integrals on the range [-1, 1] are calculated.\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Magdalena Slawinska \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:25 PM."
]
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"text": [
"Drawing associate Legendre Polynomials..\n"
]
}
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"source": [
"std::cout <<\"Drawing associate Legendre Polynomials..\" << std::endl;\n",
"TCanvas *Canvas = new TCanvas(\"DistCanvas\", \"Associate Legendre polynomials\", 10, 10, 800, 500);\n",
"Canvas->Divide(2,1);\n",
"TLegend *leg1 = new TLegend(0.5, 0.7, 0.8, 0.89);\n",
"TLegend *leg2 = new TLegend(0.5, 0.7, 0.8, 0.89);"
]
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"-------------------------------------------\n",
"drawing the set of Legendre functions"
]
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"TF1* L[5];\n",
"\n",
"L[0]= new TF1(\"L_0\", \"ROOT::Math::assoc_legendre(1, 0,x)\", -1, 1);\n",
"L[1]= new TF1(\"L_1\", \"ROOT::Math::assoc_legendre(1, 1,x)\", -1, 1);\n",
"L[2]= new TF1(\"L_2\", \"ROOT::Math::assoc_legendre(2, 0,x)\", -1, 1);\n",
"L[3]= new TF1(\"L_3\", \"ROOT::Math::assoc_legendre(2, 1,x)\", -1, 1);\n",
"L[4]= new TF1(\"L_4\", \"ROOT::Math::assoc_legendre(2, 2,x)\", -1, 1);\n",
"\n",
"TF1* SL[5];\n",
"\n",
"SL[0]= new TF1(\"SL_0\", \"ROOT::Math::sph_legendre(1, 0,x)\", -TMath::Pi(), TMath::Pi());\n",
"SL[1]= new TF1(\"SL_1\", \"ROOT::Math::sph_legendre(1, 1,x)\", -TMath::Pi(), TMath::Pi());\n",
"SL[2]= new TF1(\"SL_2\", \"ROOT::Math::sph_legendre(2, 0,x)\", -TMath::Pi(), TMath::Pi());\n",
"SL[3]= new TF1(\"SL_3\", \"ROOT::Math::sph_legendre(2, 1,x)\", -TMath::Pi(), TMath::Pi());\n",
"SL[4]= new TF1(\"SL_4\", \"ROOT::Math::sph_legendre(2, 2,x)\", -TMath::Pi(), TMath::Pi() );\n",
"\n",
"Canvas->cd(1);\n",
"gPad->SetGrid();\n",
"gPad->SetFillColor(kWhite);\n",
"L[0]->SetMaximum(3);\n",
"L[0]->SetMinimum(-2);\n",
"L[0]->SetTitle(\"Associate Legendre Polynomials\");\n",
"for (int nu = 0; nu < 5; nu++) {\n",
" L[nu]->SetLineStyle(kSolid);\n",
" L[nu]->SetLineWidth(2);\n",
" L[nu]->SetLineColor(nu+1);\n",
"}\n",
"\n",
"leg1->AddEntry(L[0]->DrawCopy(), \" P^{1}_{0}(x)\", \"l\");\n",
"leg1->AddEntry(L[1]->DrawCopy(\"same\"), \" P^{1}_{1}(x)\", \"l\");\n",
"leg1->AddEntry(L[2]->DrawCopy(\"same\"), \" P^{2}_{0}(x)\", \"l\");\n",
"leg1->AddEntry(L[3]->DrawCopy(\"same\"), \" P^{2}_{1}(x)\", \"l\");\n",
"leg1->AddEntry(L[4]->DrawCopy(\"same\"), \" P^{2}_{2}(x)\", \"l\");\n",
"leg1->Draw();\n",
"\n",
"Canvas->cd(2);\n",
"gPad->SetGrid();\n",
"gPad->SetFillColor(kWhite);\n",
"SL[0]->SetMaximum(1);\n",
"SL[0]->SetMinimum(-1);\n",
"SL[0]->SetTitle(\"Spherical Legendre Polynomials\");\n",
"for (int nu = 0; nu < 5; nu++) {\n",
" SL[nu]->SetLineStyle(kSolid);\n",
" SL[nu]->SetLineWidth(2);\n",
" SL[nu]->SetLineColor(nu+1);\n",
"}\n",
"\n",
"leg2->AddEntry(SL[0]->DrawCopy(), \" P^{1}_{0}(x)\", \"l\");\n",
"leg2->AddEntry(SL[1]->DrawCopy(\"same\"), \" P^{1}_{1}(x)\", \"l\");\n",
"leg2->AddEntry(SL[2]->DrawCopy(\"same\"), \" P^{2}_{0}(x)\", \"l\");\n",
"leg2->AddEntry(SL[3]->DrawCopy(\"same\"), \" P^{2}_{1}(x)\", \"l\");\n",
"leg2->AddEntry(SL[4]->DrawCopy(\"same\"), \" P^{2}_{2}(x)\", \"l\");\n",
"leg2->Draw();"
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"integration"
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"text": [
"Calculating integrals of Associate Legendre Polynomials on [-1, 1]\n",
"Integral [-1,1] for Associated Legendre Polynomial of Degree 0\t = \t0\n",
"Integral [-1,1] for Associated Legendre Polynomial of Degree 1\t = \t1.5708\n",
"Integral [-1,1] for Associated Legendre Polynomial of Degree 2\t = \t5.55112e-17\n",
"Integral [-1,1] for Associated Legendre Polynomial of Degree 3\t = \t0\n",
"Integral [-1,1] for Associated Legendre Polynomial of Degree 4\t = \t4\n"
]
}
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"std::cout << \"Calculating integrals of Associate Legendre Polynomials on [-1, 1]\" << std::endl;\n",
"double integral[5];\n",
"for (int nu = 0; nu < 5; nu++) {\n",
" integral[nu] = L[nu]->Integral(-1.0, 1.0);\n",
" std::cout <<\"Integral [-1,1] for Associated Legendre Polynomial of Degree \" << nu << \"\\t = \\t\" << integral[nu] << std::endl;\n",
"}"
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"Draw all canvases "
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