.世界杯预测神_『网址:687.vii』世界杯预选赛完整视频_b5p6v3_y0aqso2ym

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21: 1.15 Summability Methods

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1.15.50 $${𝐼}^{\alpha }f(x)=\sum _{k=0}^{\mathrm{\infty }}\frac{k!}{\mathrm{\Gamma }\left(k+\alpha +1\right)}{a}_k{x}^{k+\alpha }.$$

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $!$: factorial (as in $n!$), $k$: integer and ${𝐼}^{\alpha }$: fractional integral

Referenced by:

Erratum (V1.0.14) for Subsections 1.15(vi), 1.15(vii), 2.6(iii)

Permalink:

http://dlmf.nist.gov/1.15.E50

Encodings:

pMML, png, TeX

See also:

Annotations for §1.15(vi), §1.15 and Ch.1

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§1.15(vii) Fractional Derivatives

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1.15.51 $${𝐷}^{\alpha }f(x)=\frac{d^n}{{dx}^n}{𝐼}^{n-\alpha }f(x),$$

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Defines:

${𝐷}^{\alpha }$: fractional derivative (locally)

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $n$: nonnegative integer and ${𝐼}^{\alpha }$: fractional integral

Referenced by:

§1.15(vii)

Permalink:

http://dlmf.nist.gov/1.15.E51

Encodings:

pMML, png, TeX

See also:

Annotations for §1.15(vii), §1.15 and Ch.1

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1.15.52 $${𝐷}^k{𝐼}^{\alpha }={𝐷}^n{𝐼}^{\alpha +n-k},$$ $k=1,2,\mathrm{\dots },n$.

ⓘ

Symbols:

$k$: integer, $n$: nonnegative integer, ${𝐼}^{\alpha }$: fractional integral and ${𝐷}^{\alpha }$: fractional derivative

Referenced by:

§1.15(vii)

Permalink:

http://dlmf.nist.gov/1.15.E52

Encodings:

pMML, png, TeX

See also:

Annotations for §1.15(vii), §1.15 and Ch.1

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1.15.53 $${𝐷}^{\alpha }{𝐷}^{\beta }={𝐷}^{\alpha +\beta }.$$

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Symbols:

${𝐷}^{\alpha }$: fractional derivative

Permalink:

http://dlmf.nist.gov/1.15.E53

Encodings:

pMML, png, TeX

See also:

Annotations for §1.15(vii), §1.15 and Ch.1

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22: 11.10 Anger–Weber Functions

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§11.10(vii) Special Values

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11.10.25 ${𝐉}_{\nu }\left(0\right)={\displaystyle \frac{\sin \left(\pi \nu \right)}{\pi \nu }},$ ${𝐄}_{\nu }\left(0\right)={\displaystyle \frac{1-\cos \left(\pi \nu \right)}{\pi \nu }}.$

ⓘ

Symbols:

${𝐉}_{\nu }\left(z\right)$: Anger function, ${𝐄}_{\nu }\left(z\right)$: Weber function, $\pi$: the ratio of the circumference of a circle to its diameter, $\cos z$: cosine function, $\sin z$: sine function and $\nu$: real or complex order

Referenced by:

§11.10(vii)

Permalink:

http://dlmf.nist.gov/11.10.E25

Encodings:

pMML, pMML, png, png, TeX, TeX

See also:

Annotations for §11.10(vii), §11.10 and Ch.11

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11.10.26 ${𝐄}_0\left(z\right)=-{𝐇}_0\left(z\right),$ ${𝐄}_1\left(z\right)={\displaystyle \frac{2}{\pi }}-{𝐇}_1\left(z\right).$

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Symbols:

${𝐇}_{\nu }\left(z\right)$: Struve function, ${𝐄}_{\nu }\left(z\right)$: Weber function, $\pi$: the ratio of the circumference of a circle to its diameter and $z$: complex variable

Referenced by:

§11.10(vii)

Permalink:

http://dlmf.nist.gov/11.10.E26

Encodings:

pMML, pMML, png, png, TeX, TeX

See also:

Annotations for §11.10(vii), §11.10 and Ch.11

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11.10.27 $${\frac{\partial }{\partial \nu }{𝐉}_{\nu }\left(z\right)|}_{\nu =0}=\frac{1}{2}\pi {𝐇}_0\left(z\right),$$

ⓘ

Symbols:

${𝐉}_{\nu }\left(z\right)$: Anger function, ${𝐇}_{\nu }\left(z\right)$: Struve function, $\pi$: the ratio of the circumference of a circle to its diameter, $\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $z$: complex variable and $\nu$: real or complex order

Referenced by:

§11.10(vii)

Permalink:

http://dlmf.nist.gov/11.10.E27

Encodings:

pMML, png, TeX

See also:

Annotations for §11.10(vii), §11.10 and Ch.11

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11.10.29 $${𝐉}_n\left(z\right)=J_n\left(z\right),$$ $n\in \mathbb{Z}$.

ⓘ

Symbols:

${𝐉}_{\nu }\left(z\right)$: Anger function, $J_{\nu }\left(z\right)$: Bessel function of the first kind, $\in$: element of, $\mathbb{Z}$: set of all integers, $z$: complex variable and $n$: integer order

A&S Ref:

12.3.2

Referenced by:

§11.10(vii), §11.11(ii)

Permalink:

http://dlmf.nist.gov/11.10.E29

Encodings:

pMML, png, TeX

See also:

Annotations for §11.10(vii), §11.10 and Ch.11

…

23: 13.2 Definitions and Basic Properties

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§13.2(vii) Connection Formulas

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13.2.39 $$M(a,b,z)={\mathrm{e}}^{z}M(b-a,b,-z),$$

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Symbols:

$M(a,b,z)$: $={}_1{}^{}F_1^{}(a;b;z)$ Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm and $z$: complex variable

A&S Ref:

13.1.27

Referenced by:

§13.12, §13.8(i), §13.9(ii), §18.17(vi)

Permalink:

http://dlmf.nist.gov/13.2.E39

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13

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13.2.40 $$U(a,b,z)=z^{1-b}U(a-b+1,2-b,z).$$

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Symbols:

$U(a,b,z)$: Kummer confluent hypergeometric function and $z$: complex variable

A&S Ref:

13.1.29

Referenced by:

§13.8(iii)

Permalink:

http://dlmf.nist.gov/13.2.E40

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13

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13.2.41 $$\frac{1}{\mathrm{\Gamma }\left(b\right)}M(a,b,z)=\frac{{\mathrm{e}}^{\mp a\pi \mathrm{i}}}{\mathrm{\Gamma }\left(b-a\right)}U(a,b,z)+\frac{{\mathrm{e}}^{\pm (b-a)\pi \mathrm{i}}}{\mathrm{\Gamma }\left(a\right)}{\mathrm{e}}^{z}U(b-a,b,{\mathrm{e}}^{\pm \pi \mathrm{i}}z).$$

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $M(a,b,z)$: $={}_1{}^{}F_1^{}(a;b;z)$ Kummer confluent hypergeometric function, $U(a,b,z)$: Kummer confluent hypergeometric function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit and $z$: complex variable

Referenced by:

§13.12, §13.14(vii), §13.4(i), §13.7(ii)

Permalink:

http://dlmf.nist.gov/13.2.E41

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13

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13.2.42 $$U(a,b,z)=\frac{\mathrm{\Gamma }\left(1-b\right)}{\mathrm{\Gamma }\left(a-b+1\right)}M(a,b,z)+\frac{\mathrm{\Gamma }\left(b-1\right)}{\mathrm{\Gamma }\left(a\right)}{z}^{1-b}M(a-b+1,2-b,z).$$

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $M(a,b,z)$: $={}_1{}^{}F_1^{}(a;b;z)$ Kummer confluent hypergeometric function, $U(a,b,z)$: Kummer confluent hypergeometric function and $z$: complex variable

A&S Ref:

13.1.3 (in different form)

Referenced by:

§13.14(vii), §13.2(ii), §13.6(v), §13.9(ii), §33.13

Permalink:

http://dlmf.nist.gov/13.2.E42

Encodings:

pMML, png, TeX

See also:

Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13

24: 28.4 Fourier Series

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§28.4(vii) Asymptotic Forms for Large $m$

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28.4.24 $$\frac{A_{2m}^{2n}(q)}{A_0^{2n}(q)}=\frac{{(-1)}^m}{{(m!)}^2}{\left(\frac{q}{4}\right)}^m\frac{\pi \left(1+O\left(m^{-1}\right)\right)}{w_{\text{II}}(\frac{1}{2}\pi ;a_{2n}\left(q\right),q)},$$

ⓘ

Symbols:

$O\left(x\right)$: order not exceeding, $a_n\left(q\right)$: eigenvalues of Mathieu equation, $\pi$: the ratio of the circumference of a circle to its diameter, $!$: factorial (as in $n!$), $m$: integer, $q=h^2$: parameter, $n$: integer, $w_{\text{II}}(z;a,q)$: fundamental solution and $A_m(q)$: Fourier coefficient

Permalink:

http://dlmf.nist.gov/28.4.E24

Encodings:

pMML, png, TeX

See also:

Annotations for §28.4(vii), §28.4 and Ch.28

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28.4.25 $$\frac{A_{2m+1}^{2n+1}(q)}{A_1^{2n+1}(q)}=\frac{{(-1)}^{m+1}}{{\left({\left(\frac{1}{2}\right)}_{m+1}\right)}^2}{\left(\frac{q}{4}\right)}^{m+1}\frac{2\left(1+O\left(m^{-1}\right)\right)}{w_{\text{II}}^{\prime }(\frac{1}{2}\pi ;a_{2n+1}\left(q\right),q)},$$

ⓘ

Symbols:

$O\left(x\right)$: order not exceeding, $a_n\left(q\right)$: eigenvalues of Mathieu equation, ${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $\pi$: the ratio of the circumference of a circle to its diameter, $m$: integer, $q=h^2$: parameter, $n$: integer, $w(z)$: Mathieu’s equation solution and $A_m(q)$: Fourier coefficient

Permalink:

http://dlmf.nist.gov/28.4.E25

Encodings:

pMML, png, TeX

See also:

Annotations for §28.4(vii), §28.4 and Ch.28

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28.4.26 $$\frac{B_{2m+1}^{2n+1}(q)}{B_1^{2n+1}(q)}=\frac{{(-1)}^m}{{\left({\left(\frac{1}{2}\right)}_{m+1}\right)}^2}{\left(\frac{q}{4}\right)}^{m+1}\frac{2\left(1+O\left(m^{-1}\right)\right)}{w_{\text{I}}(\frac{1}{2}\pi ;b_{2n+1}\left(q\right),q)},$$

ⓘ

Symbols:

$O\left(x\right)$: order not exceeding, $b_n\left(q\right)$: eigenvalues of Mathieu equation, ${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $\pi$: the ratio of the circumference of a circle to its diameter, $m$: integer, $q=h^2$: parameter, $n$: integer, $w_{\text{I}}(z;a,q)$: fundamental solution and $B_m(q)$: Fourier coefficient

Permalink:

http://dlmf.nist.gov/28.4.E26

Encodings:

pMML, png, TeX

See also:

Annotations for §28.4(vii), §28.4 and Ch.28

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28.4.27 $$\frac{B_{2m}^{2n+2}(q)}{B_2^{2n+2}(q)}=\frac{{(-1)}^m}{{(m!)}^2}{\left(\frac{q}{4}\right)}^m\frac{q\pi \left(1+O\left(m^{-1}\right)\right)}{w_{\text{I}}^{\prime }(\frac{1}{2}\pi ;b_{2n+2}\left(q\right),q)}.$$

ⓘ

Symbols:

$O\left(x\right)$: order not exceeding, $b_n\left(q\right)$: eigenvalues of Mathieu equation, $\pi$: the ratio of the circumference of a circle to its diameter, $!$: factorial (as in $n!$), $m$: integer, $q=h^2$: parameter, $n$: integer, $w(z)$: Mathieu’s equation solution and $B_m(q)$: Fourier coefficient

Permalink:

http://dlmf.nist.gov/28.4.E27

Encodings:

pMML, png, TeX

See also:

Annotations for §28.4(vii), §28.4 and Ch.28

…

25: 12.14 The Function $W(a,x)$

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§12.14(vii) Relations to Other Functions

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12.14.13 $$W(0,\pm x)=2^{-\frac{5}{4}}\sqrt{\pi x}\left(J_{-\frac{1}{4}}\left(\frac{1}{4}{x}^2\right)\mp J_{\frac{1}{4}}\left(\frac{1}{4}{x}^2\right)\right),$$

ⓘ

Symbols:

$J_{\nu }\left(z\right)$: Bessel function of the first kind, $\pi$: the ratio of the circumference of a circle to its diameter, $W(a,x)$: parabolic cylinder function and $x$: real variable

A&S Ref:

19.25.4 (corrected)

Referenced by:

§36.2(ii)

Permalink:

http://dlmf.nist.gov/12.14.E13

Encodings:

pMML, png, TeX

See also:

Annotations for §12.14(vii), §12.14(vii), §12.14 and Ch.12

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12.14.14 $$\frac{d}{dx}W(0,\pm x)=-2^{-\frac{9}{4}}x\sqrt{\pi x}\left(J_{\frac{3}{4}}\left(\frac{1}{4}{x}^2\right)\pm J_{-\frac{3}{4}}\left(\frac{1}{4}{x}^2\right)\right).$$

ⓘ

Symbols:

$J_{\nu }\left(z\right)$: Bessel function of the first kind, $\pi$: the ratio of the circumference of a circle to its diameter, $\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $W(a,x)$: parabolic cylinder function and $x$: real variable

A&S Ref:

19.25.5

Permalink:

http://dlmf.nist.gov/12.14.E14

Encodings:

pMML, png, TeX

See also:

Annotations for §12.14(vii), §12.14(vii), §12.14 and Ch.12

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12.14.15 $$w_1(a,x)={\mathrm{e}}^{-\frac{1}{4}\mathrm{i}{x}^2}M(\frac{1}{4}-\frac{1}{2}\mathrm{i}a,\frac{1}{2},\frac{1}{2}\mathrm{i}{x}^2)={\mathrm{e}}^{\frac{1}{4}\mathrm{i}{x}^2}M(\frac{1}{4}+\frac{1}{2}\mathrm{i}a,\frac{1}{2},-\frac{1}{2}\mathrm{i}{x}^2),$$

ⓘ

Symbols:

$M(a,b,z)$: $={}_1{}^{}F_1^{}(a;b;z)$ Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $x$: real variable, $a$: real or complex parameter and $w_1(a,x)$: even solution

A&S Ref:

19.25.1 (modification of)

Referenced by:

§12.14(v)

Permalink:

http://dlmf.nist.gov/12.14.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §12.14(vii), §12.14(vii), §12.14 and Ch.12

… ►uniformly for $t\in [-1+\delta ,\mathrm{\infty })$, with $\zeta$, $\varphi (\zeta )$, $A_s(\zeta )$, and $B_s(\zeta )$ as in §12.10(vii). …

26: 1.9 Calculus of a Complex Variable

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§1.9(vii) Inversion of Limits

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1.9.64

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Symbols:

$z$: variable, $m$: nonnegative integer, $n$: nonnegative integer, $ϵ$: positive number and $\left|x\right|$: absolute value of $x$

Permalink:

http://dlmf.nist.gov/1.9.E64

Encodings:

pMML, png, TeX

See also:

Annotations for §1.9(vii), §1.9(vii), §1.9 and Ch.1

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1.9.66 $$z_{p,q}=\sum _{m=0}^p\sum _{n=0}^q{\zeta }_{m,n}.$$

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Symbols:

$z$: variable, $m$: nonnegative integer, $n$: nonnegative integer and ${\zeta }_{p,q}$: sum

Permalink:

http://dlmf.nist.gov/1.9.E66

Encodings:

pMML, png, TeX

See also:

Annotations for §1.9(vii), §1.9(vii), §1.9 and Ch.1

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1.9.69

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Symbols:

$dx$: differential of $x$ , $\int$: integral, $n$: nonnegative integer and $\left|x\right|$: absolute value of $x$

Referenced by:

§1.9(vii)

Permalink:

http://dlmf.nist.gov/1.9.E69

Encodings:

pMML, png, TeX

See also:

Annotations for §1.9(vii), §1.9(vii), §1.9 and Ch.1

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1.9.71 $${\int }_a^b\sum _{n=0}^{\mathrm{\infty }}{f}_n(t)dt=\sum _{n=0}^{\mathrm{\infty }}{\int }_a^b{f}_n(t)dt.$$

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Symbols:

$dx$: differential of $x$ , $\int$: integral and $n$: nonnegative integer

Referenced by:

§1.9(vii)

Permalink:

http://dlmf.nist.gov/1.9.E71

Encodings:

pMML, png, TeX

See also:

Annotations for §1.9(vii), §1.9(vii), §1.9 and Ch.1

27: 8.9 Continued Fractions

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8.9.2 $$z^{-a}{\mathrm{e}}^z\mathrm{\Gamma }(a,z)=\frac{z^{-1}}{1+}\frac{(1-a)z^{-1}}{1+}\frac{z^{-1}}{1+}\frac{(2-a)z^{-1}}{1+}\frac{2z^{-1}}{1+}\frac{(3-a)z^{-1}}{1+}\frac{3z^{-1}}{1+}\mathrm{\cdots },$$ .

ⓘ

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{\Gamma }(a,z)$: incomplete gamma function, $\mathrm{ph}$: phase, $z$: complex variable and $a$: parameter

Referenced by:

§8.19(vii)

Permalink:

http://dlmf.nist.gov/8.9.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §8.9 and Ch.8

…

28: 33.13 Complex Variable and Parameters

… ►The functions $F_{\mathrm{\ell }}(\eta ,\rho )$, $G_{\mathrm{\ell }}(\eta ,\rho )$, and $H_{\mathrm{\ell }}^{\pm }(\eta ,\rho )$ may be extended to noninteger values of $\mathrm{\ell }$ by generalizing $(2\mathrm{\ell }+1)!=\mathrm{\Gamma }\left(2\mathrm{\ell }+2\right)$, and supplementing (33.6.5) by a formula derived from (33.2.8) with $U(a,b,z)$ expanded via (13.2.42). … ►The quantities $C_{\mathrm{\ell }}\left(\eta \right)$, ${\sigma }_{\mathrm{\ell }}\left(\eta \right)$, and $R_{\mathrm{\ell }}$, given by (33.2.6), (33.2.10), and (33.4.1), respectively, must be defined consistently so that ►

33.13.1 $$C_{\mathrm{\ell }}\left(\eta \right)=2^{\mathrm{\ell }}{\mathrm{e}}^{\mathrm{i}{\sigma }_{\mathrm{\ell }}\left(\eta \right)-(\pi \eta /2)}\mathrm{\Gamma }\left(\mathrm{\ell }+1-\mathrm{i}\eta \right)/\mathrm{\Gamma }\left(2\mathrm{\ell }+2\right),$$

ⓘ

Symbols:

$C_{\mathrm{\ell }}\left(\eta \right)$: normalizing constant for Coulomb radial functions, ${\sigma }_{\mathrm{\ell }}\left(\eta \right)$: Coulomb phase shift, $\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\mathrm{\ell }$: nonnegative integer and $\eta$: real parameter

Permalink:

http://dlmf.nist.gov/33.13.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §33.13 and Ch.33

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33.13.2 $$R_{\mathrm{\ell }}=(2\mathrm{\ell }+1)C_{\mathrm{\ell }}\left(\eta \right)/C_{\mathrm{\ell }-1}\left(\eta \right).$$

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Symbols:

$C_{\mathrm{\ell }}\left(\eta \right)$: normalizing constant for Coulomb radial functions, $\mathrm{\ell }$: nonnegative integer, $\eta$: real parameter and $R_{\mathrm{\ell }}$: factor

Permalink:

http://dlmf.nist.gov/33.13.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §33.13 and Ch.33

…

29: 34.3 Basic Properties: $\mathit{3}j$ Symbol

… ►

§34.3(vii) Relations to Legendre Polynomials and Spherical Harmonics

… ►

34.3.19

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Symbols:

$P_n\left(x\right)$: Legendre polynomial, $\cos z$: cosine function, : $\mathit{3}j$ symbol and $l,l_r$: non-negative integers or non-negative integers plus one half.

Referenced by:

§14.18(iv), §14.30(iii), §34.3(vii)

Permalink:

http://dlmf.nist.gov/34.3.E19

Encodings:

pMML, png, TeX

See also:

Annotations for §34.3(vii), §34.3 and Ch.34

►

34.3.20

ⓘ

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\overline{z}$: complex conjugate, $Y_{l,m}(\theta ,\varphi )$: spherical harmonic, : $\mathit{3}j$ symbol and $l,l_r$: non-negative integers or non-negative integers plus one half.

Permalink:

http://dlmf.nist.gov/34.3.E20

Encodings:

pMML, png, TeX

Notational Change (effective with 1.0.19):

As a notational clarification, the spherical harmonic in the sum over $l,m$ has been explicity marked up as a complex conjugate.

See also:

Annotations for §34.3(vii), §34.3 and Ch.34

►

34.3.21

ⓘ

Symbols:

$P_n\left(x\right)$: Legendre polynomial, $\pi$: the ratio of the circumference of a circle to its diameter, $\cos z$: cosine function, $dx$: differential of $x$ , $\int$: integral, $\sin z$: sine function, : $\mathit{3}j$ symbol and $l,l_r$: non-negative integers or non-negative integers plus one half.

Referenced by:

§14.17(iv)

Permalink:

http://dlmf.nist.gov/34.3.E21

Encodings:

pMML, png, TeX

See also:

Annotations for §34.3(vii), §34.3 and Ch.34

►

34.3.22

ⓘ

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\int$: integral, $\sin z$: sine function, $Y_{l,m}(\theta ,\varphi )$: spherical harmonic, : $\mathit{3}j$ symbol and $l,l_r$: non-negative integers or non-negative integers plus one half.

Referenced by:

§14.30(ii), §34.3(vii)

Permalink:

http://dlmf.nist.gov/34.3.E22

Encodings:

pMML, png, TeX

See also:

Annotations for §34.3(vii), §34.3 and Ch.34

…

30: 3.6 Linear Difference Equations

… ►In practice, however, problems of severe instability often arise and in §§3.6(ii)–3.6(vii) we show how these difficulties may be overcome. … ►

§3.6(vii) Linear Difference Equations of Other Orders

… ►

3.6.17 $$a_n{w}_{n+1}-b_n{w}_n=d_n.$$

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Symbols:

$w_n$: sequence, $a_n$: coefficient, $b_n$: coefficient and $d_n$: coefficient

Permalink:

http://dlmf.nist.gov/3.6.E17

Encodings:

pMML, png, TeX

See also:

Annotations for §3.6(vii), §3.6 and Ch.3

… ►

3.6.18 $$a_{n,k}{w}_{n+k}+a_{n,k-1}{w}_{n+k-1}+\mathrm{\cdots }+a_{n,0}{w}_n=d_n,$$

ⓘ

Symbols:

$w_n$: sequence, $a_n$: coefficient and $d_n$: coefficient

Permalink:

http://dlmf.nist.gov/3.6.E18

Encodings:

pMML, png, TeX

See also:

Annotations for §3.6(vii), §3.6 and Ch.3

…