"에르미트 다항식(Hermite polynomials)"의 두 판 사이의 차이

수학노트
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
 
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
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<math>H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}e^{-x^2}</math>
  
 
 
 
 
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<h5 style="margin: 0px; line-height: 2em;">목록</h5>
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H_0(x)=1<br> H_1(x)=2 x<br> H_2(x)=-2+4 x^2<br> H_3(x)=-12 x+8 x^3<br> H_4(x)=12-48 x^2+16 x^4<br> H_5(x)=120 x-160 x^3+32 x^5<br> H_6(x)=-120+720 x^2-480 x^4+64 x^6<br> H_7(x)=-1680 x+3360 x^3-1344 x^5+128 x^7<br> H_8(x)=1680-13440 x^2+13440 x^4-3584 x^6+256 x^8<br> H_9(x)=30240 x-80640 x^3+48384 x^5-9216 x^7+512 x^9<br> H_10(x)=-30240+302400 x^2-403200 x^4+161280 x^6-23040 x^8+1024 x^10<br> H_11(x)=-665280 x+2217600 x^3-1774080 x^5+506880 x^7-56320 x^9+2048 x^11<br> H_12(x)=665280-7983360 x^2+13305600 x^4-7096320 x^6+1520640 x^8-135168 x^10+4096 x^12<br> H_13(x)=17297280 x-69189120 x^3+69189120 x^5-26357760 x^7+4392960 x^9-319488 x^11+8192 x^13<br> H_14(x)=-17297280+242161920 x^2-484323840 x^4+322882560 x^6-92252160 x^8+12300288 x^10-745472 x^12+16384 x^14<br> H_15(x)=-518918400 x+2421619200 x^3-2905943040 x^5+1383782400 x^7-307507200 x^9+33546240 x^11-1720320 x^13+32768 x^15<br> H_16(x)=518918400-8302694400 x^2+19372953600 x^4-15498362880 x^6+5535129600 x^8-984023040 x^10+89456640 x^12-3932160 x^14+65536 x^16<br> H_17(x)=17643225600 x-94097203200 x^3+131736084480 x^5-75277762560 x^7+20910489600 x^9-3041525760 x^11+233963520 x^13-8912896 x^15+131072 x^17<br> H_18(x)=-17643225600+317578060800 x^2-846874828800 x^4+790416506880 x^6-338749931520 x^8+75277762560 x^10-9124577280 x^12+601620480 x^14-20054016 x^16+262144 x^18<br> H_19(x)=-670442572800 x+4022655436800 x^3-6436248698880 x^5+4290832465920 x^7-1430277488640 x^9+260050452480 x^11-26671841280 x^13+1524105216 x^15-44826624 x^17+524288 x^19<br> H_20(x)=670442572800-13408851456000 x^2+40226554368000 x^4-42908324659200 x^6+21454162329600 x^8-5721109954560 x^10+866834841600 x^12-76205260800 x^14+3810263040 x^16-99614720 x^18+1048576 x^20
  
 
 
 
 
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* [http://ko.wikipedia.org/wiki/%EC%97%90%EB%A5%B4%EB%AF%B8%ED%8A%B8_%EB%8B%A4%ED%95%AD%EC%8B%9D http://ko.wikipedia.org/wiki/에르미트_다항식]
 
* [http://ko.wikipedia.org/wiki/%EC%97%90%EB%A5%B4%EB%AF%B8%ED%8A%B8_%EB%8B%A4%ED%95%AD%EC%8B%9D http://ko.wikipedia.org/wiki/에르미트_다항식]
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* [http://ko.wikipedia.org/wiki/%EC%96%91%EC%9E%90%EC%A1%B0%ED%99%94%EC%A7%84%EB%8F%99%EC%9E%90 http://ko.wikipedia.org/wiki/양자조화진동자]
 
* http://en.wikipedia.org/wiki/Hermite_polynomials
 
* http://en.wikipedia.org/wiki/Hermite_polynomials
 
* http://www.wolframalpha.com/input/?i=
 
* http://www.wolframalpha.com/input/?i=

2009년 12월 20일 (일) 19:22 판

이 항목의 스프링노트 원문주소

 

 

개요

\(H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}e^{-x^2}\)

 

 

목록

H_0(x)=1
H_1(x)=2 x
H_2(x)=-2+4 x^2
H_3(x)=-12 x+8 x^3
H_4(x)=12-48 x^2+16 x^4
H_5(x)=120 x-160 x^3+32 x^5
H_6(x)=-120+720 x^2-480 x^4+64 x^6
H_7(x)=-1680 x+3360 x^3-1344 x^5+128 x^7
H_8(x)=1680-13440 x^2+13440 x^4-3584 x^6+256 x^8
H_9(x)=30240 x-80640 x^3+48384 x^5-9216 x^7+512 x^9
H_10(x)=-30240+302400 x^2-403200 x^4+161280 x^6-23040 x^8+1024 x^10
H_11(x)=-665280 x+2217600 x^3-1774080 x^5+506880 x^7-56320 x^9+2048 x^11
H_12(x)=665280-7983360 x^2+13305600 x^4-7096320 x^6+1520640 x^8-135168 x^10+4096 x^12
H_13(x)=17297280 x-69189120 x^3+69189120 x^5-26357760 x^7+4392960 x^9-319488 x^11+8192 x^13
H_14(x)=-17297280+242161920 x^2-484323840 x^4+322882560 x^6-92252160 x^8+12300288 x^10-745472 x^12+16384 x^14
H_15(x)=-518918400 x+2421619200 x^3-2905943040 x^5+1383782400 x^7-307507200 x^9+33546240 x^11-1720320 x^13+32768 x^15
H_16(x)=518918400-8302694400 x^2+19372953600 x^4-15498362880 x^6+5535129600 x^8-984023040 x^10+89456640 x^12-3932160 x^14+65536 x^16
H_17(x)=17643225600 x-94097203200 x^3+131736084480 x^5-75277762560 x^7+20910489600 x^9-3041525760 x^11+233963520 x^13-8912896 x^15+131072 x^17
H_18(x)=-17643225600+317578060800 x^2-846874828800 x^4+790416506880 x^6-338749931520 x^8+75277762560 x^10-9124577280 x^12+601620480 x^14-20054016 x^16+262144 x^18
H_19(x)=-670442572800 x+4022655436800 x^3-6436248698880 x^5+4290832465920 x^7-1430277488640 x^9+260050452480 x^11-26671841280 x^13+1524105216 x^15-44826624 x^17+524288 x^19
H_20(x)=670442572800-13408851456000 x^2+40226554368000 x^4-42908324659200 x^6+21454162329600 x^8-5721109954560 x^10+866834841600 x^12-76205260800 x^14+3810263040 x^16-99614720 x^18+1048576 x^20

 

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