北大数学物理方法(A)-数学物理方程教案10柱函数2

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Outline1›ùμê()ÔnÆ2007cSC.S.Wu1›ùμê()OutlineùLJ:1μêμê½ÂHankel¼ê2Bessel¼êA^Bessel§Š¯K ÎNe% ‚²¡»•ÄC.S.Wu1›ùμê()OutlineùLJ:1μêμê½ÂHankel¼ê2Bessel¼êA^Bessel§Š¯K ÎNe% ‚²¡»•ÄC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsReferencesÇÂÁ§5êÆÔn{6§§17.5ù&œ§5êÆÔn{6§§11.2nÎ!X1Á§5êÆÔn{6§§13.2C.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsùLJ:1μêμê½ÂHankel¼ê2Bessel¼êA^Bessel§Š¯K ÎNe% ‚²¡»•ÄC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Â÷v4í'Xddz[zνCν(z)]=zνCν−1(z)ddzz−νCν(z)=−z−νCν+1(z)¼ê{Cν(z)}Ú¡Î¼êJν(z)´Î¼ê§¡1˜aμêNν(z)´Î¼ê§¡1aμꌱy²µÎ¼ê˜½´Bessel§)Jν(z)ÚNν(z)‚5|ܧ´Ä„´Î¼êºC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Â÷v4í'Xddz[zνCν(z)]=zνCν−1(z)ddzz−νCν(z)=−z−νCν+1(z)¼ê{Cν(z)}Ú¡Î¼êJν(z)´Î¼ê§¡1˜aμêNν(z)´Î¼ê§¡1aμꌱy²µÎ¼ê˜½´Bessel§)Jν(z)ÚNν(z)‚5|ܧ´Ä„´Î¼êºC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Â÷v4í'Xddz[zνCν(z)]=zνCν−1(z)ddzz−νCν(z)=−z−νCν+1(z)¼ê{Cν(z)}Ú¡Î¼êJν(z)´Î¼ê§¡1˜aμêNν(z)´Î¼ê§¡1aμꌱy²µÎ¼ê˜½´Bessel§)Jν(z)ÚNν(z)‚5|ܧ´Ä„´Î¼êºC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Â÷v4í'Xddz[zνCν(z)]=zνCν−1(z)ddzz−νCν(z)=−z−νCν+1(z)¼ê{Cν(z)}Ú¡Î¼êJν(z)´Î¼ê§¡1˜aμêNν(z)´Î¼ê§¡1aμꌱy²µÎ¼ê˜½´Bessel§)Jν(z)ÚNν(z)‚5|ܧ´Ä„´Î¼êºC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Â÷v4í'Xddz[zνCν(z)]=zνCν−1(z)ddzz−νCν(z)=−z−νCν+1(z)¼ê{Cν(z)}Ú¡Î¼êJν(z)´Î¼ê§¡1˜aμêNν(z)´Î¼ê§¡1aμꌱy²µÎ¼ê˜½´Bessel§)Jν(z)ÚNν(z)‚5|ܧ´Ä„´Î¼êºC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsùLJ:1μêμê½ÂHankel¼ê2Bessel¼êA^Bessel§Š¯K ÎNe% ‚²¡»•ÄC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsµc¡0 Jν(z)ÚNν(z)ь±^5£Ρŧ§‚ìCÐm©O´Jν(z)∼r2πzcosz−νπ2−π4Nν(z)∼r2πzsinz−νπ2−π4§‚£Ρť§QkuÑŧqk¬àÅXJ?n¯K¥§9uÑŽ¬àŧ½‡¦²(«©uÑŽ¬àŧùü‡¼êÒؐBC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsµc¡0 Jν(z)ÚNν(z)ь±^5£Ρŧ§‚ìCÐm©O´Jν(z)∼r2πzcosz−νπ2−π4Nν(z)∼r2πzsinz−νπ2−π4§‚£Ρť§QkuÑŧqk¬àÅXJ?n¯K¥§9uÑŽ¬àŧ½‡¦²(«©uÑŽ¬àŧùü‡¼êÒؐBC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Âùžw,AŠ‚5|ÜH(1)ν(z)≡Jν(z)+iNν(z)∼r2πzexphiz−νπ2−π4iH(2)ν(z)≡Jν(z)−iNν(z)∼r2πzexph−iz−νπ2−π4iXJÜþƒAžmÏfe−iωt§KH(1)ν(z)“LuÑŧH(2)ν(z)“L¬àÅC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctions½Âùžw,AŠ‚5|ÜH(1)ν(z)≡Jν(z)+iNν(z)∼r2πzexphiz−νπ2−π4iH(2)ν(z)≡Jν(z)−iNν(z)∼r2πzexph−iz−νπ2−π4iXJÜþƒAžmÏfe−iωt§KH(1)ν(z)“LuÑŧH(2)ν(z)“L¬àÅC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsH(1)ν(z)¡1˜«Hankel¼êH(2)ν(z)¡1«Hankel¼êH(1)ν(z)ÚH(2)ν(z)Ñ´Bessel§)§Ñ´Î¼ê½¡1naμêC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsH(1)ν(z)¡1˜«Hankel¼êH(2)ν(z)¡1«Hankel¼êH(1)ν(z)ÚH(2)ν(z)Ñ´Bessel§)§Ñ´Î¼ê½¡1naμêC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsH(1)ν(z)¡1˜«Hankel¼êH(2)ν(z)¡1«Hankel¼êH(1)ν(z)ÚH(2)ν(z)Ñ´Bessel§)§Ñ´Î¼ê½¡1naμêC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsDefinitionofCylindricalFunctionsHankelFunctionsH(1)ν(z)¡1˜«Hankel¼êH(2)ν(z)¡1«Hankel¼êH(1)ν(z)ÚH(2)ν(z)Ñ´Bessel§)§Ñ´Î¼ê½¡1naμêC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsEigenproblemsInvolvingBesselEqCoolingofCylindricalBodyPlaneRadialOscillationofCircularRingùLJ:1μêμê½ÂHankel¼ê2Bessel¼êA^Bessel§Š¯K ÎNe% ‚²¡»•ÄC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsEigenproblemsInvolvingBesselEqCoolingofCylindricalBodyPlaneRadialOscillationofCircularRing~10.1läN¯K\ç?ØBessel§Š¯K¦o±½ /kªÇµãù‡¯KØÓuL?ØL ‡©§½)¯Kµy3¿vk‰ÑЩ^‡§¤‡¦Ø´£ /Ä £XۑžmژmCzy3‡¦´kªÇ−−−‰½ ‡©§Ú.^‡e¤kˆ«ÄªªÇ´Ïy3¯K¥¿vk‰ÑЩ^‡§¤±ØUÑ £=ÄØC(ØC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsEigenproblemsInvolvingBesselEqCoolingofCylindricalBodyPlaneRadialOscillationofCircularRing~10.1läN¯K\ç?ØBessel§Š¯K¦o±½ /kªÇµãù‡¯KØÓuL?ØL ‡©§½)¯Kµy3¿vk‰ÑЩ^‡§¤‡¦Ø´£ /Ä £XۑžmژmCzy3‡¦´kªÇ−−−‰½ ‡©§Ú.^‡e¤kˆ«ÄªªÇ´Ïy3¯K¥¿vk‰ÑЩ^‡§¤±ØUÑ £=ÄØC(ØC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsEigenproblemsInvolvingBesselEqCoolingofCylindricalBodyPlaneRadialOscillationofCircularRing~10.1läN¯K\ç?ØBessel§Š¯K¦o±½ /kªÇµãù‡¯KØÓuL?ØL ‡©§½)¯Kµy3¿vk‰ÑЩ^‡§¤‡¦Ø´£ /Ä £XۑžmژmCzy3‡¦´kªÇ−−−‰½ ‡©§Ú.^‡e¤kˆ«ÄªªÇ´Ïy3¯K¥¿vk‰ÑЩ^‡§¤±ØUÑ £=ÄØC(ØC.S.Wu1›ùμê()CylindricalFunctionsApplicationsofBesselftnsEigen

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