„Anal2-magic” változatai közötti eltérés

245. sor:

Analitikus fuggveny: egy intervallumon ananlitikus egy fuggveny, ha ott eloallitja a T-sora

=== Nevezetes fuggvenyek T-sorai ===

<math>\frac {x^m} {1-x} = \sum_{k=m}^{n} x^k ~~-->~~ Konvergencia tartomany: |x| < 1 </math>

<math>\frac {x^m} {1-x} = \sum_{k=m}^{\infty} x^k \rightarrow Konvergencia tartomany: |x| < 1 </math>

<math>e^x = \sum_{k=0}^{\infty} \frac {x^k} { k!} \rightarrow KT: x \in R </math>

<math>ln(1+x) = -\sum_{k=1}^{\infty} (-1)^k \frac{x^{k}}{k} \rightarrow KT :|x| < 1 </math>

<math>(1 + x)^a = \sum_{k=0}^{n} \binom{a}{k}* x^k ~~-->~~ |x| < 1, a \in C </math>

<math>(1 + x)^a = \sum_{k=0}^{\infty} \binom{a}{k}* x^k \rightarrow |x| < 1, a \in C </math>

<math>\sin(x) = \sum_{k=0}^{\infty} \frac {-1^k} {(2 * k + 1)!} * x^{2 * k + 1} \rightarrow KT: x \in R</math>

<math>\cos(x) = \sum_{k=0}^{\infty} \frac {-1^k} {(2 * k)!} * x^{2 * k } \rightarrow KT: x \in R </math>

<math>\sinh(x) = \sum_{k=0}^{\infty} \frac {1} {(2 * k+1)!} * x^{2 * k + 1} \rightarrow KT: x \in R </math>

<math>\cosh(x) = \sum_{k=0}^{\infty} \frac {1} {(2 * k)!} * x^{2 * k } \rightarrow KT: x \in R </math>

=== Lagrange-hiba becsles ===

@@ 245. sor: / 245. sor: @@
 Analitikus fuggveny: egy intervallumon ananlitikus egy fuggveny, ha ott eloallitja a T-sora<br />
 === Nevezetes fuggvenyek T-sorai ===
-<math>\frac {x^m} {1-x} = \sum_{k=m}^{n} x^k  --> Konvergencia tartomany: |x| < 1 </math> <br />
+<math>\frac {x^m} {1-x} = \sum_{k=m}^{\infty} x^k  \rightarrow Konvergencia tartomany: |x| < 1 </math> <br />
-<math>e^x = \sum_{k=0}^{n} \frac {x^k} { k!}  --> KT: x \in R </math> <br />
+<math>e^x = \sum_{k=0}^{\infty} \frac {x^k} { k!} \rightarrow KT: x \in R </math> <br />
-<math>ln(1+x) = \sum_{k=0}^{n} \frac{-1^k}{(k+1)!}* x^{k+1}  --> KT :|x| < 1 </math> <br />
+<math>ln(1+x) = -\sum_{k=1}^{\infty} (-1)^k \frac{x^{k}}{k} \rightarrow KT :|x| < 1 </math> <br />
-<math>(1 + x)^a = \sum_{k=0}^{n} \binom{a}{k}* x^k  --> |x| < 1, a \in C </math> <br />
+<math>(1 + x)^a = \sum_{k=0}^{\infty} \binom{a}{k}* x^k  \rightarrow |x| < 1, a \in C </math> <br />
-<math>\sin(x) = \sum_{k=0}^{n} \frac {-1^k} {(2 * k + 1)!} * x^{2 * k + 1}   --> KT: x \in R</math><br />
+<math>\sin(x) = \sum_{k=0}^{\infty} \frac {-1^k} {(2 * k + 1)!} * x^{2 * k + 1}   \rightarrow KT: x \in R</math><br />
-<math>\cos(x) = \sum_{k=0}^{n} \frac {-1^k} {(2 * k)!} * x^{2 * k }   --> KT: x \in R </math><br />
+<math>\cos(x) = \sum_{k=0}^{\infty} \frac {-1^k} {(2 * k)!} * x^{2 * k }   \rightarrow KT: x \in R </math><br />
-<math>\sinh(x) = \sum_{k=0}^{n} \frac {1} {(2 * k+1)!} * x^{2 * k + 1}   --> KT: x \in R </math><br />
+<math>\sinh(x) = \sum_{k=0}^{\infty} \frac {1} {(2 * k+1)!} * x^{2 * k + 1}   \rightarrow KT: x \in R </math><br />
-<math>\cosh(x) = \sum_{k=0}^{n} \frac {1} {(2 * k)!} * x^{2 * k }   --> KT: x \in R </math><br />
+<math>\cosh(x) = \sum_{k=0}^{\infty} \frac {1} {(2 * k)!} * x^{2 * k }  \rightarrow KT: x \in R </math><br />
 === Lagrange-hiba becsles ===