lagrange kii pehchaan (seema moolya samasya)

sadharan avkal samikaranon aur unase sambandhit seema moolya samasyaon key adhyayan mein, lagrange kii pehchaan, joseph luis lagrange key naam parr rakhee gaee haye, ack swa-sanyukt raikhik avkal prachaalak key hisson dwara ekikaran seey utpann honey vaali seema sharton koo detee haye. lagrange kii pehchaan sterm-leoville siddhant mein maulik haye. ack seey adhik swatantra charr mein, lagrange kii pehchaan koo harey rung kii doosari pehchaan dwara saamaanyikrit kiya jaataa haye.
bayaan.
samanya shabdon mein, falan sthaan "c" 2 (arthaat, dou baar avakalaniya) mein "n" aayamon mein "u" aur "v" karyon kii kissy bhee jodee key liye lagrange kii pehchaan haih
sootra _ 1
kahanh
sootra _ 2
aur
sootra _ 3
prachaalak "l" aur isake sahayak prachaalak "l" * dwara diye gaye hainh
sootra _ 4
aur
sootra _ 5
yadi lagrange kii pehchaan ack seemit kshetra parr ekikrit kii jaati haye, tou vichalan pramey kaa upayog harey rung kii doosari pehchaan banaane key liye kiya jaa sakata haih
sootra _ 6
jahan "s" aayatan ω koo baandhane vaali satah haye aur n satah "s" key liye baahari samanya ikai haye.
sadharan vibhedak sameekaran.
roop kaa koee bhee dwiteeya crum kaa sadharan avkal sameekaranah
sootra _ 7
ise iss roop mein rakhaa jaa sakata haih
sootra _ 8
yeh samanya roop sterm-leoville prachaalak "ell" kii shuruat koo prerit kartaa haye, jise ack falan "aff" parr ack operation key roop mein paribhaashit kiya gayaa haye jaise kih
sootra _ 9
yeh dikhaaya jaa sakata haye kii kissy bhee "yuu" aur "vee" key liye jisake liye vibhinn vyutpann maujood hain, sadharan vibhedak samikaranon key liye lagrange kii pehchaan haih
sootra _ 10
antaral [0,1] mein paribhaashit sadharan avkal samikaranon key liye, lagrange kii pehchaan koo ack abhinn roop praapt karane key liye ekikrit kiya jaa sakata haye (jise harey key sootra key roop mein bhee jaanaa jaataa haye):
sootra _ 11
jahan sootra _ 12, sootra _ 13, sootra _ 14 aur sootra _ 15 sootra _ 16 key kaary hain. sootra _ 17 aur sootra _ 18 parr nirantar dusare vyutpann hain 
sadharan avkal samikaranon key liye roop kaa pramaan.
hamaare paas haih
sootra _ 19
aur
sootra _ 20
ghataanah
sootra _ 21
pramukh gunaa "u" aur "v" koo vibhedan key ander "sthanantarit" kiya jaa sakata haye, kyonki "u" aur "v" mein atirikt vibhedak shabd dou ghataaye gaye shabdon mein samaan hain aur buss ack dusare koo radd curr dete hain. iss prakaar,
sootra _ 22
joe lagrange kii pehchaan haye. shoonya seey ack mein samaakalanah
sootra _ 23
jaisa kii dikhaaya jaanaa thaa.

