User contributions
(newest | oldest) View (newer 20 | older 20) (20 | 50 | 100 | 250 | 500)
- 19:32, 15 March 2018 (diff | hist) . . (+530) . . N U n(x)=Sum (-1)^k n!/((2k+1)!(n-2k-1)!)(1-x^2)^(k+1/2)x^(n-2k-1) (Created page with "==Theorem== The following formula holds: $$U_n(x) = \displaystyle\sum_{k=0}^{\left\lfloor \frac{n-1}{2} \right\rfloor} \dfrac{(-1)^k n!}{(2k+1)!(n-2k-1)!} (1-x^2)^{k+\frac{1}{...") (current)
- 19:28, 15 March 2018 (diff | hist) . . (+58) . . T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (current)
- 19:26, 15 March 2018 (diff | hist) . . (+508) . . N T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (Created page with "==Theorem== The following formula holds: $$T_n(x) = \displaystyle\sum_{k=0}^{\left\lfloor \frac{n}{2} \right\rfloor} \dfrac{(-1)^k n!}{(2k)!(n-2k)!} (1-x^2)^k x^{n-2k},$$ wher...")
- 19:22, 15 March 2018 (diff | hist) . . (+1) . . U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (current)
- 19:22, 15 March 2018 (diff | hist) . . (-2) . . U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n
- 19:21, 15 March 2018 (diff | hist) . . (+50) . . U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n
- 19:20, 15 March 2018 (diff | hist) . . (+476) . . N U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (Created page with "==Theorem== The following formula holds: $$U_n(x) =-\dfrac{i}{2} \left[ \left( x + i \sqrt{1-x^2} \right)^n + \left( x-i\sqrt{1-x^2} \right)^n \right],$$ where $U_n$ denotes [...")
- 19:18, 15 March 2018 (diff | hist) . . (+456) . . N T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n (Created page with "==Theorem== The following formula holds: $$T_n(x)=\dfrac{\left(x+i\sqrt{1-x^2} \right)^n+\left(x-i\sqrt{1-x^2} \right)^n}{2},$$ where $T_n$ denotes Chebyshev T and $i$ den...") (current)
- 19:15, 15 March 2018 (diff | hist) . . (+50) . . Chebyshev U
- 19:01, 15 March 2018 (diff | hist) . . (+54) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 19:00, 15 March 2018 (diff | hist) . . (+120) . . Chebyshev U
- 19:00, 15 March 2018 (diff | hist) . . (+120) . . Chebyshev T
- 14:42, 15 March 2018 (diff | hist) . . (+34) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 14:42, 15 March 2018 (diff | hist) . . (+115) . . Hypergeometric pFq (current)
- 14:39, 15 March 2018 (diff | hist) . . (+214) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 14:37, 15 March 2018 (diff | hist) . . (-433) . . Laguerre L (current)
- 14:36, 15 March 2018 (diff | hist) . . (+348) . . N L n'(x)=-Sum L k(x) (Created page with "==Theorem== The following formula holds: $$L_n'(x) = -\displaystyle\sum_{k=0}^{n-1} L_k(x),$$ where $L_n$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|...") (current)
- 14:35, 15 March 2018 (diff | hist) . . (+356) . . N XL n'(x)=nL n(x)-n L (n-1)(x) (Created page with "==Theorem== The following formula holds: $$xL_n'(x)=nL_n(x)-nL_{n-1}(x),$$ where $L_n$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|Special Functions f...") (current)
- 14:32, 15 March 2018 (diff | hist) . . (+23) . . (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (current)
- 14:32, 15 March 2018 (diff | hist) . . (+343) . . N (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (Created page with "==Theorem== The following formula holds: $$(n+1)L_{n+1}(x)=(2n+1-x)L_n(x)-nL_{n-1}(x),$$ where $L_{n+1}$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|S...")
(newest | oldest) View (newer 20 | older 20) (20 | 50 | 100 | 250 | 500)