"체비셰프 다항식"의 두 판 사이의 차이
| 1번째 줄: | 1번째 줄: | ||
<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%;">이 항목의 스프링노트 원문주소</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%;">이 항목의 스프링노트 원문주소</h5> | ||
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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%;"> | + | <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%;">제1종 체비세프 다항식</h5> |
* <math>T_n(x)</math><br> | * <math>T_n(x)</math><br> | ||
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<h5 style="margin: 0px; line-height: 2em;">목록</h5> | <h5 style="margin: 0px; line-height: 2em;">목록</h5> | ||
| − | 1<br> x<br> -1+2 x^2<br> -3 x+4 x^3<br> 1-8 x^2+8 x^4<br> 5 x-20 x^3+16 x^5<br> -1+18 x^2-48 x^4+32 x^6<br> -7 x+56 x^3-112 x^5+64 x^7<br> 1-32 x^2+160 x^4-256 x^6+128 x^8<br> 9 x-120 x^3+432 x^5-576 x^7+256 x^9<br> -1+50 x^2-400 x^4+1120 x^6-1280 x^8+512 x^10<br> -11 x+220 x^3-1232 x^5+2816 x^7-2816 x^9+1024 x^11<br> 1-72 x^2+840 x^4-3584 x^6+6912 x^8-6144 x^10+2048 x^12<br> 13 x-364 x^3+2912 x^5-9984 x^7+16640 x^9-13312 x^11+4096 x^13<br> -1+98 x^2-1568 x^4+9408 x^6-26880 x^8+39424 x^10-28672 x^12+8192 x^14<br> -15 x+560 x^3-6048 x^5+28800 x^7-70400 x^9+92160 x^11-61440 x^13+16384 x^15<br> 1-128 x^2+2688 x^4-21504 x^6+84480 x^8-180224 x^10+212992 x^12-131072 x^14+32768 x^16<br> 17 x-816 x^3+11424 x^5-71808 x^7+239360 x^9-452608 x^11+487424 x^13-278528 x^15+65536 x^17<br> -1+162 x^2-4320 x^4+44352 x^6-228096 x^8+658944 x^10-1118208 x^12+1105920 x^14-589824 x^16+131072 x^18<br> -19 x+1140 x^3-20064 x^5+160512 x^7-695552 x^9+1770496 x^11-2723840 x^13+2490368 x^15-1245184 x^17+262144 x^19<br> 1-200 x^2+6600 x^4-84480 x^6+549120 x^8-2050048 x^10+4659200 x^12-6553600 x^14+5570560 x^16-2621440 x^18+524288 x^20 | + | T_0[x]=1<br> T_1[x]=x<br> T_2[x]=-1+2 x^2<br> T_3[x]=-3 x+4 x^3<br> T_4[x]=1-8 x^2+8 x^4<br> T_5[x]=5 x-20 x^3+16 x^5<br> T_6[x]=-1+18 x^2-48 x^4+32 x^6<br> T_7[x]=-7 x+56 x^3-112 x^5+64 x^7<br> T_8[x]=1-32 x^2+160 x^4-256 x^6+128 x^8<br> T_9[x]=9 x-120 x^3+432 x^5-576 x^7+256 x^9<br> T_10[x]=-1+50 x^2-400 x^4+1120 x^6-1280 x^8+512 x^10<br> T_11[x]=-11 x+220 x^3-1232 x^5+2816 x^7-2816 x^9+1024 x^11<br> T_12[x]=1-72 x^2+840 x^4-3584 x^6+6912 x^8-6144 x^10+2048 x^12<br> T_13[x]=13 x-364 x^3+2912 x^5-9984 x^7+16640 x^9-13312 x^11+4096 x^13<br> T_14[x]=-1+98 x^2-1568 x^4+9408 x^6-26880 x^8+39424 x^10-28672 x^12+8192 x^14<br> T_15[x]=-15 x+560 x^3-6048 x^5+28800 x^7-70400 x^9+92160 x^11-61440 x^13+16384 x^15<br> T_16[x]=1-128 x^2+2688 x^4-21504 x^6+84480 x^8-180224 x^10+212992 x^12-131072 x^14+32768 x^16<br> T_17[x]=17 x-816 x^3+11424 x^5-71808 x^7+239360 x^9-452608 x^11+487424 x^13-278528 x^15+65536 x^17<br> T_18[x]=-1+162 x^2-4320 x^4+44352 x^6-228096 x^8+658944 x^10-1118208 x^12+1105920 x^14-589824 x^16+131072 x^18<br> T_19[x]=-19 x+1140 x^3-20064 x^5+160512 x^7-695552 x^9+1770496 x^11-2723840 x^13+2490368 x^15-1245184 x^17+262144 x^19<br> T_20[x]=1-200 x^2+6600 x^4-84480 x^6+549120 x^8-2050048 x^10+4659200 x^12-6553600 x^14+5570560 x^16-2621440 x^18+524288 x^20 |
2009년 11월 22일 (일) 07:29 판
이 항목의 스프링노트 원문주소
제1종 체비세프 다항식
- \(T_n(x)\)
- \(n \geq 0 \) 에 대하여 \(\cos n\theta = T_n(\cos\theta)\)를 만족시키는 다항식 \(T_n(x)\)을 정의
목록
T_0[x]=1
T_1[x]=x
T_2[x]=-1+2 x^2
T_3[x]=-3 x+4 x^3
T_4[x]=1-8 x^2+8 x^4
T_5[x]=5 x-20 x^3+16 x^5
T_6[x]=-1+18 x^2-48 x^4+32 x^6
T_7[x]=-7 x+56 x^3-112 x^5+64 x^7
T_8[x]=1-32 x^2+160 x^4-256 x^6+128 x^8
T_9[x]=9 x-120 x^3+432 x^5-576 x^7+256 x^9
T_10[x]=-1+50 x^2-400 x^4+1120 x^6-1280 x^8+512 x^10
T_11[x]=-11 x+220 x^3-1232 x^5+2816 x^7-2816 x^9+1024 x^11
T_12[x]=1-72 x^2+840 x^4-3584 x^6+6912 x^8-6144 x^10+2048 x^12
T_13[x]=13 x-364 x^3+2912 x^5-9984 x^7+16640 x^9-13312 x^11+4096 x^13
T_14[x]=-1+98 x^2-1568 x^4+9408 x^6-26880 x^8+39424 x^10-28672 x^12+8192 x^14
T_15[x]=-15 x+560 x^3-6048 x^5+28800 x^7-70400 x^9+92160 x^11-61440 x^13+16384 x^15
T_16[x]=1-128 x^2+2688 x^4-21504 x^6+84480 x^8-180224 x^10+212992 x^12-131072 x^14+32768 x^16
T_17[x]=17 x-816 x^3+11424 x^5-71808 x^7+239360 x^9-452608 x^11+487424 x^13-278528 x^15+65536 x^17
T_18[x]=-1+162 x^2-4320 x^4+44352 x^6-228096 x^8+658944 x^10-1118208 x^12+1105920 x^14-589824 x^16+131072 x^18
T_19[x]=-19 x+1140 x^3-20064 x^5+160512 x^7-695552 x^9+1770496 x^11-2723840 x^13+2490368 x^15-1245184 x^17+262144 x^19
T_20[x]=1-200 x^2+6600 x^4-84480 x^6+549120 x^8-2050048 x^10+4659200 x^12-6553600 x^14+5570560 x^16-2621440 x^18+524288 x^20
재미있는 사실
역사
메모
관련된 항목들
수학용어번역
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Chebyshev_polynomials
- http://en.wikipedia.org/wiki/
- http://www.wolframalpha.com/input/?i=Chebyshev+polynomials
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
관련도서 및 추천도서
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)