User contributions
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
- 22:30, 19 December 2017 (diff | hist) . . (+382) . . N Orthogonality of Chebyshev T on (-1,1) (Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$: $$\int_{-1}^1 \dfrac{T_m(x)T_n(x)}{\sqrt{1-x^2}} dx = \left\{ \begin{array}{ll} 0 &; m \neq n \\ \dfrac...")
- 22:15, 19 December 2017 (diff | hist) . . (-346) . . Chebyshev T (→Properties)
- 22:14, 19 December 2017 (diff | hist) . . (+77) . . T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (current)
- 22:13, 19 December 2017 (diff | hist) . . (+170) . . N T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (Created page with "==Theorem== The following formula holds for $n=0,1,2,\ldots$: $$T_{n+1}(x)-2xT_n(x)+T_{n-1}(x)=0.$$ ==Proof== ==References== Category:Theorem Category:Unproven")
- 22:13, 19 December 2017 (diff | hist) . . (0) . . Chebyshev T (→Properties)
- 22:12, 19 December 2017 (diff | hist) . . (-466) . . Chebyshev T
- 22:10, 19 December 2017 (diff | hist) . . (+114) . . Book:T.S. Chihara/An Introduction to Orthogonal Polynomials
- 22:09, 19 December 2017 (diff | hist) . . (+54) . . Cosine (current)
- 22:09, 19 December 2017 (diff | hist) . . (+33) . . Orthogonality relation for cosine on (0,pi)
- 22:08, 19 December 2017 (diff | hist) . . (+364) . . N Orthogonality relation for cosine on (0,pi) (Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0.$$ ==Proof== ==References==...")
- 22:07, 19 December 2017 (diff | hist) . . (+361) . . N 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$: $$2\cos(mt)\cos(nt)=\cos((m+n)t)+\cos((m-n)t),$$ where $\cos$ denotes cosine. ==Proof== ==Referen...") (current)
- 22:03, 19 December 2017 (diff | hist) . . (+50) . . Cosine
- 22:02, 19 December 2017 (diff | hist) . . (+2,060) . . N Book:T.S. Chihara/An Introduction to Orthogonal Polynomials (Created page with "{{Book|An Introduction to Orthogonal Polynomials|1978|Gordon and Breach||T.S. Chihara}} === Contents === :PREFACE :CHAPTER I. ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS ::1...")
- 20:06, 14 December 2017 (diff | hist) . . (-31) . . Main Page (→Special functions)
- 20:00, 14 December 2017 (diff | hist) . . (0) . . File:Signumglyph.png (Tom uploaded a new version of File:Signumglyph.png) (current)
- 19:59, 14 December 2017 (diff | hist) . . (0) . . File:Signumglyph.png (Tom uploaded a new version of File:Signumglyph.png)
- 19:52, 14 December 2017 (diff | hist) . . (-1) . . Signum (replaced image with correct one for sgn(x))
- 19:51, 14 December 2017 (diff | hist) . . (+732) . . N File:Signumplot.png (<pre> #!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 10, 10 x1=np.arange(-4,-0.05,0.01); x2=np.arange(0.05,4,0.01); def g1(x): return -1 def g2(x):...) (current)
- 01:54, 26 November 2017 (diff | hist) . . (+196) . . Bernstein B (current)
- 01:13, 26 November 2017 (diff | hist) . . (+22) . . Bernstein B (→External links)
- 01:13, 26 November 2017 (diff | hist) . . (+129) . . Bernstein B
- 01:11, 26 November 2017 (diff | hist) . . (+211) . . N Bernstein B (Created page with "The Bernstein polynomials $B_k^n(x)$ are defined by $$B_k^n(x)={n \choose k} x^k (1-x)^{n-k},$$ where ${n \choose k}$ denotes a Binomial coefficient. =Properties= =Refer...")
- 12:22, 7 November 2017 (diff | hist) . . (-7) . . Main Page (→Polynomials)
- 12:22, 7 November 2017 (diff | hist) . . (+7) . . Main Page (→Polynomials)
- 12:22, 7 November 2017 (diff | hist) . . (+22) . . Main Page (→Polynomials)
- 19:55, 4 November 2017 (diff | hist) . . (+304) . . Struve function
- 19:53, 4 November 2017 (diff | hist) . . (+1) . . Integral representation of Struve function (3) (current)
- 16:29, 4 November 2017 (diff | hist) . . (+438) . . N Derivative of Struve H0 (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_0'(z) = \dfrac{2}{\pi} - \mathbf{H}_1(z),$$ where $\mathbf{H}$ denotes the Struve function. ==Proof== ==References=...")
- 16:27, 4 November 2017 (diff | hist) . . (+549) . . N Recurrence relation for Struve function (2) (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\nu-1}(z)-\mathbf{H}_{\nu+1}(z) = 2\mathbf{H}_{\nu}'(z) - \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\frac{3}{2})},$$ w...") (current)
- 16:26, 4 November 2017 (diff | hist) . . (+43) . . Recurrence relation for Struve fuction (current)
- 16:25, 4 November 2017 (diff | hist) . . (+547) . . N Recurrence relation for Struve fuction (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\nu-1}(z)+\mathbf{H}_{\nu+1}(z) = \dfrac{2\nu}{z} \mathbf{H}_{\nu}(z) + \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\fra...")
- 16:23, 4 November 2017 (diff | hist) . . (+560) . . Integral representation of Struve function (3)
- 16:17, 4 November 2017 (diff | hist) . . (+252) . . N Integral representation of Struve function (3) (Created page with "==Theorem== ==Proof== ==References== * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral representation of Stru...")
- 16:14, 4 November 2017 (diff | hist) . . (+699) . . N Integral representation of Struve function (2) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(\nu)>-\dfrac{1}{2}$: $$\mathbf{H}_{\nu}(z) = \dfrac{z^{\nu}}{2^{\nu-1}\sqrt{\pi}\Gamma(\nu+\frac{1}{2})} \displaystyle...") (current)
- 16:11, 4 November 2017 (diff | hist) . . (+1) . . Integral representation of Struve function (current)
- 16:11, 4 November 2017 (diff | hist) . . (+632) . . N Integral representation of Struve function (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(\nu) > - \dfrac{1}{2}$: $$\mathbf{H}_{\nu}(z) = \dfrac{z^{\nu}}{2^{\nu-1}\sqrt{\pi}\Gamma(\nu+\frac{1}{2})} \displayst...")
- 22:58, 31 October 2017 (diff | hist) . . (+803) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:40, 31 October 2017 (diff | hist) . . (+32) . . Struve function
- 01:15, 29 October 2017 (diff | hist) . . (+775) . . Main Page
- 00:28, 29 October 2017 (diff | hist) . . (+123) . . Main Page (→Error function and friends)
- 00:27, 29 October 2017 (diff | hist) . . (+847) . . N File:Dawsondplusglyph.png (<pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams import scipy.special rcParams['figure.figsize'] = 2.4,2.4 x1=np.arange(-15,15,0.001) f=np.vectorize(lambda x: scipy.special.dawsn...) (current)
- 00:21, 29 October 2017 (diff | hist) . . (+105) . . Dawson D+ (current)
- 00:20, 29 October 2017 (diff | hist) . . (+518) . . N File:Dawsondplusplot.png (Category:Plot <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams import scipy.special rcParams['figure.figsize'] = 10, 10 x=np.arange(-15,15,0.001); f=np.vectorize(lambda x: sc...) (current)
- 00:12, 29 October 2017 (diff | hist) . . (-1) . . Dawson D- (current)
- 00:12, 29 October 2017 (diff | hist) . . (+9) . . Dawson D+
- 00:11, 29 October 2017 (diff | hist) . . (-118) . . Clausen sine
- 00:03, 29 October 2017 (diff | hist) . . (0) . . Clausen sine
- 00:01, 29 October 2017 (diff | hist) . . (+118) . . Clausen sine
- 23:00, 28 October 2017 (diff | hist) . . (+4,594) . . N Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (Created page with "__NOTOC__ {{Book|Formulas and Theorems for the Special Functions of Mathematical Physics |1966|Springer-Verlag||Wilhelm Magnus|author2 = Fritz Oberhettinger|author3=Raj Pal S...")
- 22:01, 28 October 2017 (diff | hist) . . (+1) . . Main Page (→Bessel functions and friends)
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
