Kalkulus II. J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">1. Line\303\241ris algebra</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">2. T\303\266bbv\303\241ltoz\303\263s f\303\274ggv\303\251nyek</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">3. F\303\274ggv\303\251nysorozatok \303\251s f\303\274ggv\303\251nysorok</Font></Text-field>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">3.1. Pontonk\303\251nti \303\251s egyenletes konvergencia</Font></Text-field> restart;
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.1. F\303\274ggv\303\251nyterek, f\303\274ggv\303\251nysorozatok.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.2. Cauchy-krit\303\251rium f\303\274ggv\303\251nysorozatokra.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.3. F\303\274ggv\303\251nysorok.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.4. Weierstrass-krit\303\251rium.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.5. Hat\303\241r\303\241tmenetek felcser\303\251l\303\251se.</Font></Text-field> limit(limit(n/(n+m),n=infinity),m=infinity); limit(limit(n/(n+m),m=infinity),n=infinity); IiIi IiIh
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.6. T\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.7. P\303\251lda.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.8. P\303\251lda.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">*3.1.9. Monoton konvergencia t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">*3.1.10. Domin\303\241lt konvergencia t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.11. K\303\266vetkezm\303\251ny: hat\303\241r\303\241tmenet \303\251s integr\303\241l felcser\303\251l\303\251se.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.12. K\303\266vetkezm\303\251ny.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.13. P\303\251lda.</Font></Text-field> limit(n*x*(1-x^2)^n,n=infinity) assuming(0<x, x<1); IiIh int(n*x*(1-x^2)^n,x=0..1) assuming(n::posint); LCQqKCMiIiIiIiNGJUkibkc2IkYlLCZGJ0YlRiVGJSEiIkYl limit(n^2*x*(1-x^2)^n,n=infinity) assuming(0<x, x<1); IiIh int(n^2*x*(1-x^2)^n,x=0..1) assuming(n::posint); LCQqKCMiIiIiIiNGJSlJIm5HNiJGJkYlLCZGKEYlRiVGJSEiIkYl
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.14. Bevezet\305\221 p\303\251lda.</Font></Text-field> f:=sin(n*x)/n^(1/2); limit(f,n=infinity); KiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomSSJuR0YoIiIiSSJ4R0YoRixGLClGKyNGLCIiIyEiIg== IiIh diff(f,x); limit(%,n=infinity); KiYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomSSJuR0YoIiIiSSJ4R0YoRixGLClGKyNGLCIiI0Ys SSp1bmRlZmluZWRHJSpwcm90ZWN0ZWRH
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.1.15. F\303\274ggv\303\251nysorozat tagonk\303\251nti differenci\303\241l\303\241sa.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">*3.1.16. T\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">*3.1.17. Weierstrass approxim\303\241ci\303\263s t\303\251tele.</Font></Text-field> f:=x->sin(Pi*x); B:=(n,x)->sum(binomial(n,k)*f(k/n)*x^k*(1-x)^(n-k),k=0..n); Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJkkjUGlHRiwiIiJGJEYxRiVGJUYl Zio2JEkibkc2IkkieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkc3VtR0YlNiQqKi1JKWJpbm9taWFsRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiRGJEkia0dGJSIiIi1JImZHRiU2IyomRjRGNUYkISIiRjUpRiZGNEY1KSwmRjVGNUYmRjosJkYkRjVGNEY6RjUvRjQ7IiIhRiRGJUYlRiU= plot({f(x),B(2,x),B(10,x),B(30,x)},x=0..1); 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
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">3.2. Hatv\303\241nysorok</Font></Text-field> restart;
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.1. Defin\303\255ci\303\263.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.2. Cauchy-Hadamard-t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.3. Defin\303\255ci\303\263.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.4. K\303\266vetkezm\303\251ny.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.5. T\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.6. Taylor-t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.7. K\303\266vetkezm\303\251ny.</Font></Text-field> sum(x^n,n=0..infinity); sum(x^n/n,n=1..infinity); sum(x^n/n^2,n=1..infinity); series(%%%,x=0); series(%%%,x=0); series(%%%,x=0); LCQqJCwmSSJ4RzYiIiIiRichIiJGKEYo LCQtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYiIiJGK0kieEdGKCEiIkYt LUkocG9seWxvZ0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkIiIjSSJ4R0Yn KzFJInhHNiIiIiIiIiFGJUYlRiUiIiNGJSIiJEYlIiIlRiUiIiYtSSJPRyUqcHJvdGVjdGVkRzYjRiUiIic= Ky9JInhHNiIiIiJGJSNGJSIiI0YnI0YlIiIkRikjRiUiIiVGKyNGJSIiJkYtLUkiT0clKnByb3RlY3RlZEc2I0YlIiIn Ky9JInhHNiIiIiJGJSNGJSIiJSIiIyNGJSIiKiIiJCNGJSIjO0YnI0YlIiNEIiImLUkiT0clKnByb3RlY3RlZEc2I0YlIiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">*3.2.8. Megjegyz\303\251s.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.9. Megjegyz\303\251s.</Font></Text-field> series(1/(1-x),x=1/2); KzEsJkkieEc2IiIiIiNGJiIiIyEiIkYoIiIhIiIlRiYiIilGKCIjOyIiJCIjS0YrIiNrIiImLUkiT0clKnByb3RlY3RlZEc2I0YmIiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.10. Az exponenci\303\241lis f\303\274ggv\303\251ny, trigonometrikus \303\251</Font>s hiperbolikus f<Font encoding="UTF-8">\303\274</Font>ggv<Font encoding="UTF-8">\303\251</Font>nyek.</Text-field> sum(z^n/n!,n=0..infinity); exp(z); exp(z1+z2); expand(%); LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkjejFHRiciIiJJI3oyR0YnRis= KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kjejFHRigiIiItRiQ2I0kjejJHRihGKw== plots[complexplot](exp(I*t),t=0..1,x=0..1,y=0..1); 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 (exp(I*z)+exp(-I*z))/2; convert(%,trig); (exp(I*z)-exp(-I*z))/(2*I); convert(%,trig); LCYqJiMiIiIiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiZeI0YlRiVJInpHRixGJUYlRiUqJkYkRiUtRig2IywkKiYsJEYvRiVGJUYwRiUhIiJGJUYl LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= LCQqJiwkKiYjIiIiIiIjRideI0YnRidGJ0YnLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomRilGJ0kiekdGMEYnRictRiw2IywkKiYsJEYpRidGJ0YzRichIiJGOUYnRjk= LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= sum((-1)^n*z^(2*n)/(2*n)!,n=0..infinity); sum((-1)^n*z^(2*n+1)/(2*n+1)!,n=0..infinity); LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= exp(I*t); convert(%,trig); LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJl4jIiIiRitJInRHRidGKw== LCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kidEdGKCIiIiomXiNGK0YrLUkkc2luR0YlRilGK0Yr cos(z)^2+sin(z)^2; simplify(%); LCYqJCktSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiekdGKiIiIyIiIkYuKiQpLUkkc2luR0YnRitGLUYuRi4= IiIi cos(z1+z2); expand(%); sin(z1+z2); expand(%); LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkjejFHRiciIiJJI3oyR0YnRis= LCYqJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSN6MUdGKSIiIi1GJTYjSSN6MkdGKUYsRiwqJi1JJHNpbkdGJkYqRiwtRjJGLkYsISIi LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkjejFHRiciIiJJI3oyR0YnRis= LCYqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSN6MUdGKSIiIi1JJGNvc0dGJjYjSSN6MkdGKUYsRiwqJi1GLkYqRiwtRiVGL0YsRiw= (exp(z)+exp(-z))/2; convert(%,trigh); (exp(z)-exp(-z))/2; convert(%,trigh); LCYqJiMiIiIiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0YsRiVGJSomRiRGJS1GKDYjLCRGLiEiIkYlRiU= LUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0Yn LCYqJiMiIiIiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0YsRiVGJSomRiRGJS1GKDYjLCRGLiEiIkYlRjM= LUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0Yn sum(z^(2*n)/(2*n)!,n=0..infinity); sum(z^(2*n+1)/(2*n+1)!,n=0..infinity); LUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0Yn LUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0Yn cosh(z)^2-sinh(z)^2; simplify(%); LCYqJCktSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRioiIiMiIiJGLiokKS1JJXNpbmhHRidGK0YtRi4hIiI= IiIi cosh(z1+z2); expand(%); sinh(z1+z2); expand(%); LUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJI3oxR0YnIiIiSSN6MkdGJ0Yr LCYqJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kjejFHRikiIiItRiU2I0kjejJHRilGLEYsKiYtSSVzaW5oR0YmRipGLC1GMkYuRixGLA== LUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJI3oxR0YnIiIiSSN6MkdGJ0Yr LCYqJi1JJXNpbmhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kjejFHRikiIiItSSVjb3NoR0YmNiNJI3oyR0YpRixGLComLUYuRipGLC1GJUYvRixGLA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.11. T\303\251tel.</Font></Text-field> plots[complexplot](exp(I*t),t=0..2*Pi-0.1,x=-1..1,y=-1..1); 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 exp(Pi*I/2); exp(Pi*I); cos(z+2*Pi); sin(z+2*Pi); XiMiIiI= ISIi LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= exp(z+2*Pi*I); expand(%); LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkiekdGJyIiIiomKiYiIiNGK14jRitGK0YrSSNQaUdGJUYrRis= LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInpHRic= cosh(z+2*Pi*I); sinh(z+2*Pi*I); LUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0Yn LUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ6R0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 3" layout="Heading 3">3.3.12. Feladat.</Text-field> plots[complexplot3d](exp(z),z=-2-2*Pi*I..2+2*Pi*I); 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<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.13. Defin\303\255ci\303\263.</Font></Text-field> ln(x+I*y); evalc(%); LUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSJ4R0YnIiIiKiZeI0YrRitJInlHRidGK0Yr LCYqJiMiIiIiIiNGJS1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJiokKUkieEdGLEYmRiVGJSokKUkieUdGLEYmRiVGJUYlRiUqJl4jRiVGJS1JJ2FyY3RhbkdGKTYkRjRGMUYlRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.14. T\303\251tel.</Font></Text-field> D(exp); D(sin); D(cos); D(sinh); D(cosh); SSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI= SSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI= LCRJJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiEiIg== SSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYi SSVzaW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYi D(tan); D(cot); D(tanh); D(coth); LCYiIiJGIyokKUkkdGFuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIjRiNGIw== LCYiIiIhIiIqJClJJGNvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiI0YjRiQ= LCYiIiJGIyokKUkldGFuaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiI0YjISIi LCYiIiJGIyokKUklY290aEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiI0YjISIi D(log); D(z->z^alpha); Zio2I0kiekc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiRGJCEiIkYlRiVGJQ== Zio2I0kiekc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKigpRiRJJmFscGhhR0YlIiIiRitGLEYkISIiRiVGJUYl
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.15. M\303\251rtani sor.</Font></Text-field> sum(z^n,n=0..infinity); LCQqJCwmSSJ6RzYiIiIiRichIiJGKEYo
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.16. A logaritmus f\303\274ggv\303\251ny hatv\303\241nysorai.</Font></Text-field> sum(z^n/n,n=1..infinity); LCQtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYiIiJGK0kiekdGKCEiIkYt sum((-1)^(n+1)*z^n/n,n=1..infinity); LUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmIiIiRipJInpHRidGKg== sum(z^(2*n+1)/(2*n+1),n=0..infinity); LCQqJiMiIiIiIiNGJS1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJiwmRiVGJUkiekdGLEYlRiUsJkYlRiVGMCEiIkYyRiVGJQ==
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.17. Az arctg f\303\274ggv\303\251ny hatv\303\241nysora.</Font></Text-field> sum((-1)^(n+1)*z^(2*n+1)/(2*n+1),n=0..infinity); KiYqJiMiIiIiIiNGJV4jRiVGJUYlLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomLCZGJUYlKiZGJ0YlSSJ6R0YtRiVGJUYlLCZGJUYlKiYsJEYnRiVGJUYyRiUhIiJGNkYl
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.18. Newton binomi\303\241lis sora.</Font></Text-field> sum(binomial(alpha,n)*z^n,n=0..infinity); KSwmIiIiRiRJInpHNiJGJEkmYWxwaGFHRiY=
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.19. Az arcsin f\303\274ggv\303\251ny hatv\303\241nysora.</Font></Text-field> sum((-1)^n*binomial(-1/2,n)*z^(2*n+1)/(2*n+1),n=0..infinity); KihJInpHNiIiIiItSSdhcmNzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyokKSokKUYjIiIjRiUjRiVGMEYlRiVGLSEiIg==
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.2.20. Hatv\303\241nysorok alkalmaz\303\241sa differenci\303\241legyenletek megold\303\241s\303\241ra.</Font></Text-field> dsolve(x^2*diff(y(x),x,x)+x*diff(y(x),x)+(x^2-n^2)*y(x)=0); Ly1JInlHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JEkibkdGJUYnRitGKyomSSRfQzJHRiVGKy1JKEJlc3NlbFlHRi5GMUYrRis=
<Text-field style="Heading 2" layout="Heading 2">3.3. Fourier-sorok</Text-field> restart;
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.1. \303\201ltal\303\241nos\303\255tott Pitagorasz-t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3">3.3.2. Fourier-sor.</Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.3. T\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.4. T\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.5. Defin\303\255ci\303\263.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.6. Defin\303\255ci\303\263.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.7. Riesz-Fischer-t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3">3.3.8. Klasszikus Fourier-sorok.</Text-field> f:=x->abs(x); l:=1/2; a0:=1/l*int(f(x),x=-l..l); a:=k->(1/l*int(f(x)*cos(Pi*k*x/l),x=-l..l) assuming(k::posint)); b:=k->(1/l*int(f(x)*sin(Pi*k*x/l),x=-l..l) assuming(k::posint)); eval(a(k)); eval(b(k)); Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkYWJzRyUqcHJvdGVjdGVkR0YjRiVGJUYl IyIiIiIiIw== IyIiIiIiIw== Zio2I0kia0c2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkpYXNzdW1pbmdHSShfc3lzbGliR0YlNiQ3IyomSSJsR0YlISIiLUkkaW50RzYkJSpwcm90ZWN0ZWRHRis2JComLUkiZkdGJTYjSSJ4R0YlIiIiLUkkY29zR0YzNiMqKkkjUGlHRjRGO0YkRjtGOkY7Ri9GMEY7L0Y6OywkRi9GMEYvRjs3IydGJEkncG9zaW50R0Y0RiVGJUYl Zio2I0kia0c2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkpYXNzdW1pbmdHSShfc3lzbGliR0YlNiQ3IyomSSJsR0YlISIiLUkkaW50RzYkJSpwcm90ZWN0ZWRHRis2JComLUkiZkdGJTYjSSJ4R0YlIiIiLUkkc2luR0YzNiMqKkkjUGlHRjRGO0YkRjtGOkY7Ri9GMEY7L0Y6OywkRi9GMEYvRjs3IydGJEkncG9zaW50R0Y0RiVGJUYl KigsJikhIiJJImtHNiIiIiJGKEYlRigpSSNQaUclKnByb3RlY3RlZEciIiNGJSlGJkYsRiU= IiIh s:=(n,x)->a0/2+sum(a(k)*cos(Pi*k*x/l)+b(k)*sin(Pi*k*x/l),k=1..n); Zio2JEkibkc2IkkieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiMiIiIiIiNGLUkjYTBHRiVGLUYtLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQsJiomLUkiYUdGJTYjSSJrR0YlRi0tSSRjb3NHRjI2IyoqSSNQaUdGM0YtRjtGLUYmRi1JImxHRiUhIiJGLUYtKiYtSSJiR0YlRjpGLS1JJHNpbkdGMkY+Ri1GLS9GOztGLUYkRi1GJUYlRiU= plot({f(x),s(2,x),s(5,x),s(10,x)},x=-l..l); 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f:=x->signum(x); l:=1/2; a0:=1/l*int(f(x),x=-l..l); a:=k->(1/l*int(f(x)*cos(Pi*k*x/l),x=-l..l) assuming(k::posint)); b:=k->(1/l*int(f(x)*sin(Pi*k*x/l),x=-l..l) assuming(k::posint)); eval(a(k)); eval(b(k)); Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUknc2lnbnVtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlRiNGJUYlRiU= IyIiIiIiIw== IiIh Zio2I0kia0c2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkpYXNzdW1pbmdHSShfc3lzbGliR0YlNiQ3IyomSSJsR0YlISIiLUkkaW50RzYkJSpwcm90ZWN0ZWRHRis2JComLUkiZkdGJTYjSSJ4R0YlIiIiLUkkY29zR0YzNiMqKkkjUGlHRjRGO0YkRjtGOkY7Ri9GMEY7L0Y6OywkRi9GMEYvRjs3IydGJEkncG9zaW50R0Y0RiVGJUYl Zio2I0kia0c2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkpYXNzdW1pbmdHSShfc3lzbGliR0YlNiQ3IyomSSJsR0YlISIiLUkkaW50RzYkJSpwcm90ZWN0ZWRHRis2JComLUkiZkdGJTYjSSJ4R0YlIiIiLUkkc2luR0YzNiMqKkkjUGlHRjRGO0YkRjtGOkY7Ri9GMEY7L0Y6OywkRi9GMEYvRjs3IydGJEkncG9zaW50R0Y0RiVGJUYl IiIh LCQqKiIiIyIiIiwmKSEiIkkia0c2IkYlRiVGKEYlSSNQaUclKnByb3RlY3RlZEdGKEYpRihGKA== plot({f(x),s(2,x),s(5,x),s(10,x)},x=-l..l); 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<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.9. T\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3">3.3.10. Dirichlet-formula.</Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.11. Lipschitz-krit\303\251rium.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.12. K\303\266vetkezm\303\251ny.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.13. K\303\266vetkezm\303\251ny: Riemann-f\303\251le lokaliz\303\241ci\303\263s t\303\251tel.</Font></Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Font encoding="UTF-8">3.3.14. Klasszikus ortogon\303\241lis polinomok.</Font></Text-field> with(orthopoly); NyhJIkdHNiJJIkhHRiRJIkxHRiRJIlBHRiRJIlRHRiRJIlVHRiQ= JacobiP(0,1,3/4,x); p0:=simplify(%,'JacobiP'); JacobiP(1,1,3/4,x); p1:=simplify(%,'JacobiP'); JacobiP(2,1,3/4,x); p2:=simplify(%,'JacobiP'); JacobiP(3,1,3/4,x); p3:=simplify(%,'JacobiP'); LUkoSmFjb2JpUEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmIiIhIiIiIyIiJCIiJUkieEdGJw== IiIi LUkoSmFjb2JpUEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmIiIiRikjIiIkIiIlSSJ4R0Yn LCYjIiIiIiIpRiQqJiMiIzpGJUYkSSJ4RzYiRiRGJA== LUkoSmFjb2JpUEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmIiIjIiIiIyIiJCIiJUkieEdGJw== LCgjIiNMIiIpISIiKiYjIiNkRiUiIiJJInhHNiJGKkYqKiYjIiRQJSIkRyJGKiksJkYrRipGKkYmIiIjRipGKg== LUkoSmFjb2JpUEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmIiIkIiIiI0YpIiIlSSJ4R0Yn LCojIiNgIiIlISIiKiYjIiNwRiUiIiJJInhHNiJGKkYqKiYjIiRAJyIjS0YqKSwmRitGKkYqRiYiIiNGKkYqKiYjIiU8ayIlQzVGKilGMiIiJEYqRio= int((1-x)^1*(1+x)^(3/4)*p1*p2,x=-1..1); IiIh P(0,x); P(1,x); P(2,x); P(3,x); IiIi SSJ4RzYi LCYjIiIiIiIjISIiKiYjIiIkRiVGJClJInhHNiJGJUYkRiQ= LCYqJiMiIiYiIiMiIiIpSSJ4RzYiIiIkRidGJyomI0YrRiZGJ0YpRichIiI= p0:=P(0,3/4,3/4,x); p1:=P(1,3/4,3/4,x); p2:=P(2,3/4,3/4,x); p3:=P(3,3/4,3/4,x); IiIi LCQqJiMiIigiIiUiIiJJInhHNiJGJ0Yn LCgjIiRAIiIjSyEiIiomIyIjKioiIzsiIiJJInhHNiJGK0YrKiYjRilGJUYrKSwmRixGK0YrRiYiIiNGK0Yr LCojIiQ6KCIjayEiIiomIyIlOj0iJEciIiIiSSJ4RzYiRitGKyomIyIlWEBGKkYrKSwmRixGK0YrRiYiIiNGK0YrKiYjRiRGKkYrKUYyIiIkRitGKw== plot({p0,p1,p2,p3},x=-1..1); 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LaguerreL(0,0,x); p0:=simplify(%,'LaguerreL'); LaguerreL(1,0,x); p1:=simplify(%,'LaguerreL'); LaguerreL(2,0,x); p2:=simplify(%,'LaguerreL'); LaguerreL(3,0,x); p3:=simplify(%,'LaguerreL'); LUkqTGFndWVycmVMRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQiIiFJInhHRic= IiIi LUkqTGFndWVycmVMRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQiIiJJInhHRic= LCYiIiJGI0kieEc2IiEiIg== LUkqTGFndWVycmVMRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQiIiNJInhHRic= LCgiIiJGIyomIiIjRiNJInhHNiJGIyEiIiomI0YjRiVGIylGJkYlRiNGIw== LUkqTGFndWVycmVMRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQiIiRJInhHRic= LCoiIiJGIyomIiIkRiNJInhHNiJGIyEiIiomI0YlIiIjRiMpRiZGK0YjRiMqJiNGIyIiJ0YjKUYmRiVGI0Yo HermiteH(0,x); p0:=simplify(%,'HermiteH'); HermiteH(1,x); p1:=simplify(%,'HermiteH'); HermiteH(2,x); p2:=simplify(%,'HermiteH'); HermiteH(3,x); p3:=simplify(%,'HermiteH'); plot({p0,p1,p2,p3},x=0..infinity); LUkpSGVybWl0ZUhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCIiIUkieEdGJw== IiIi LUkpSGVybWl0ZUhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCIiIkkieEdGJw== 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