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- 00:50, 21 December 2017 (diff | hist) . . (+484) . . N D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \left[ z^{\nu}\mathbf{H}_{\nu}(z) \right]=z^{\nu}\mathbf{H}_{\nu-1}(z),$$ where $\mathbf{H}$ denotes...")
- 00:47, 21 December 2017 (diff | hist) . . (+17) . . Derivative of Struve H0
- 00:47, 21 December 2017 (diff | hist) . . (+78) . . Struve function (→Properties)
- 01:50, 20 December 2017 (diff | hist) . . (-22) . . Main Page
- 01:49, 20 December 2017 (diff | hist) . . (0) . . Clausen cosine
- 01:46, 20 December 2017 (diff | hist) . . (+297) . . N Unsigned Lah numbers (Created page with "The unsigned Lah numbers $L(n,k)$ are defined by $$L(n,k)={{n-1} \choose {k-1}} \dfrac{n!}{k!},$$ where ${{n-1} \choose {k-1}}$ denotes a binomial coefficient and $n!$ den...") (current)
- 01:46, 20 December 2017 (diff | hist) . . (+7) . . Signed Lah numbers (current)
- 01:46, 20 December 2017 (diff | hist) . . (+43) . . Signed Lah numbers
- 01:45, 20 December 2017 (diff | hist) . . (+254) . . N Signed Lah numbers (Created page with "The signed Lah numbers $L(n,k)$ are defined by $$L(n,k)={{n-1} \choose {k-1}} \dfrac{n!}{k!},$$ where ${{n-1} \choose {k-1}}$ denotes a binomial coefficient and $n!$ denot...")
- 01:44, 20 December 2017 (diff | hist) . . (+38) . . Main Page (→Special sequences)
- 01:32, 20 December 2017 (diff | hist) . . (+250) . . N Matrix exponential (Created page with "The $n$-dimensional matrix exponential $\exp_n \colon \mathbb{R}^{n \times n} \rightarrow \mathbb{R}^{n \times n}$ is defined by $$\exp_n(X)=\displaystyle\sum_{k=0}^{\infty} \...")
- 01:29, 20 December 2017 (diff | hist) . . (+245) . . N C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x) (Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} C_n^{\lambda}(x)=2\lambda C_{n+1}^{\lambda+1}(x),$$ where $C_n^{\lambda}$ denotes Gegenbauer C....") (current)
- 01:29, 20 December 2017 (diff | hist) . . (-5) . . Gegenbauer C (→Properties) (current)
- 01:28, 20 December 2017 (diff | hist) . . (-207) . . Gegenbauer C
- 01:28, 20 December 2017 (diff | hist) . . (+260) . . N NC n^(lambda)(x)=(n-1+2lambda)xC (n-1)^(lambda)(x)-2lambda(1-x^2)C (n-2)^(lambda-1)(x) (Created page with "==Theorem== The following formula holds: $$nC_n^{\lambda}(x) = (n-1+2\lambda)xC_{n-1}^{\lambda}(x) - 2\lambda(1-x^2)C_{n-2}^{\lambda-1}(x),$$ where $C_n^{\lambda}$ denotes G...") (current)
- 01:27, 20 December 2017 (diff | hist) . . (-212) . . Gegenbauer C
- 01:26, 20 December 2017 (diff | hist) . . (+11) . . Gegenbauer C
- 01:26, 20 December 2017 (diff | hist) . . (+13) . . (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (current)
- 01:26, 20 December 2017 (diff | hist) . . (+248) . . N (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (Created page with "==Theorem== The following formula holds: $$(n+2\lambda)C_n^{\lambda}(x) = 2\lambda(C_n^{\lambda+1}(x)-xC_{n-1}^{\lambda+1}(x)),$$ where $C_n^{\lambda}$ denotes [[Gegenbauer C]...")
- 01:25, 20 December 2017 (diff | hist) . . (-211) . . Gegenbauer C (→Properties)
- 01:24, 20 December 2017 (diff | hist) . . (+11) . . Gegenbauer C
- 23:49, 19 December 2017 (diff | hist) . . (+1) . . Gegenbauer C (→Properties)
- 23:48, 19 December 2017 (diff | hist) . . (0) . . m NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (Tom moved page NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x) to NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x))) (current)
- 23:48, 19 December 2017 (diff | hist) . . (+84) . . N NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x) (Tom moved page NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x) to NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x))) (current)
- 23:48, 19 December 2017 (diff | hist) . . (+243) . . N NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (Created page with "==Theorem== The following formula holds: $$nC_n^{\lambda}(x) = 2\lambda(xC_{n-1}^{\lambda+1}(x) - C_{n-2}^{\lambda+1}(x)),$$ where $C_n^{\lambda}$ denotes Gegenbauer C. =...")
- 23:47, 19 December 2017 (diff | hist) . . (-213) . . Gegenbauer C (→Properties)
- 23:47, 19 December 2017 (diff | hist) . . (+259) . . N (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x) (Created page with "==Theorem== The following formula holds: $$(n+2)C_{n+2}^{\lambda}(x)=2(\lambda+n+1)xC_{n+1}^{\lambda}(x)-(2\lambda+n)C_n^{\lambda}(x),$$ where $C_{n+2}^{\lambda}$ denotes Ge...") (current)
- 23:46, 19 December 2017 (diff | hist) . . (-209) . . Gegenbauer C (→Properties)
- 23:45, 19 December 2017 (diff | hist) . . (+490) . . N Orthogonality of Gegenbauer C on (-1,1) (Created page with "==Theorem== The following formula holds: $$\displaystyle\int_{-1}^1 (1-x^2)^{\lambda-\frac{1}{2}} C_n^{\lambda}(x)C_m^{\lambda}(x) \mathrm{d}x = \left\{ \begin{array}{ll} 0, &...") (current)
- 23:42, 19 December 2017 (diff | hist) . . (-1,017) . . Gegenbauer C
- 23:37, 19 December 2017 (diff | hist) . . (+3,881) . . N Book:W.W. Bell/Special Functions for Scientists and Engineers (Created page with "{{Book|Special Functions for Scientists and Engineers|1968|D. Van Nostrand||W.W. Bell}} ===Contents=== :PREFACE :LIST OF SYMBOLS :Chapter 1 Series Solution of Differential Eq...")
- 23:24, 19 December 2017 (diff | hist) . . (+3,652) . . N Book:Richard Beals/Special functions, a graduate text (Created page with "{{Book|Special functions, a graduate text|2010|Cambridge University Press||Richard Beals|author2=Roderick Wong}} ===Contents=== :1 Orientation ::1.1 Power series solutions ::...")
- 22:54, 19 December 2017 (diff | hist) . . (+19) . . Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (current)
- 22:52, 19 December 2017 (diff | hist) . . (+81) . . Book:T.S. Chihara/An Introduction to Orthogonal Polynomials (current)
- 22:52, 19 December 2017 (diff | hist) . . (+32) . . Orthogonality relation for cosine on (0,pi) (current)
- 22:50, 19 December 2017 (diff | hist) . . (+9) . . Orthogonality of Chebyshev U on (-1,1) (current)
- 22:49, 19 December 2017 (diff | hist) . . (-72) . . Relationship between Chebyshev U and Gegenbauer C (current)
- 22:43, 19 December 2017 (diff | hist) . . (-82) . . Relationship between Chebyshev U and hypergeometric 2F1 (current)
- 22:42, 19 December 2017 (diff | hist) . . (+383) . . N Orthogonality of Chebyshev U on (-1,1) (Created page with "==Theorem== The following formula holds for $m, n \in \{0,1,2,\ldots\}$: $$\int_{-1}^1 \dfrac{U_m(x)U_n(x)}{\sqrt{1-x^2}} dx = \left\{ \begin{array}{ll} 0 &; m \neq n \\ \dfra...")
- 22:40, 19 December 2017 (diff | hist) . . (-264) . . Chebyshev U
- 22:38, 19 December 2017 (diff | hist) . . (+248) . . Chebyshev T
- 22:36, 19 December 2017 (diff | hist) . . (+203) . . Orthogonality of Chebyshev T on (-1,1) (current)
- 22:33, 19 December 2017 (diff | hist) . . (-11) . . Relationship between Chebyshev T and Gegenbauer C (current)
- 22:33, 19 December 2017 (diff | hist) . . (-71) . . Relationship between Chebyshev T and Gegenbauer C
- 22:32, 19 December 2017 (diff | hist) . . (+28) . . Relationship between Chebyshev T and hypergeometric 2F1 (current)
- 22:32, 19 December 2017 (diff | hist) . . (-107) . . Relationship between Chebyshev T and hypergeometric 2F1
- 22:31, 19 December 2017 (diff | hist) . . (-4) . . Chebyshev T
- 22:30, 19 December 2017 (diff | hist) . . (+18) . . Chebyshev T (→Properties)
- 22:30, 19 December 2017 (diff | hist) . . (+1) . . Orthogonality of Chebyshev T on (-1,1)
- 22:30, 19 December 2017 (diff | hist) . . (+9) . . Orthogonality of Chebyshev T on (-1,1)
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