Git commit 0332375b86ecbf23166212730149df8ce89d7109 by Stefan Gerlach. Committed on 06/04/2015 at 10:23. Pushed by sgerlach into branch 'master'.
improved handbook special functions M +31 -31 doc/index.docbook http://commits.kde.org/labplot/0332375b86ecbf23166212730149df8ce89d7109 diff --git a/doc/index.docbook b/doc/index.docbook index 9a2a4aa..b0179c0 100644 --- a/doc/index.docbook +++ b/doc/index.docbook @@ -823,13 +823,13 @@ For more information about the functions see the documentation of GSL. <row><entry>k1s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of first order, exp(x) k<subscript>1</subscript>(x)</action></entry></row> <row><entry>k2s(x)</entry><entry><action>scaled irregular modified spherical Bessel function of second order, exp(x) k<subscript>2</subscript>(x)</action></entry></row> <row><entry>kls(l,x)</entry><entry><action>scaled irregular modified spherical Bessel function of order l, exp(x) k<subscript>l</subscript>(x)</action></entry></row> -<row><entry>Jnu(nu,x)</entry><entry><action>regular cylindrical Bessel function of fractional order nu, J<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Ynu(nu,x)</entry><entry><action>irregular cylindrical Bessel function of fractional order nu, Y<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Inu(nu,x)</entry><entry><action>regular modified Bessel function of fractional order nu, I<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Inus(nu,x)</entry><entry><action>scaled regular modified Bessel function of fractional order nu, exp(-|x|) I<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>Knu(nu,x)</entry><entry><action>irregular modified Bessel function of fractional order nu, K<subscript>ν</subscript>(x)</action></entry></row> -<row><entry>lnKnu(nu,x)</entry><entry><action>logarithm of the irregular modified Bessel function of fractional order nu,ln(K<subscript>ν</subscript>(x))</action></entry></row> -<row><entry>Knus(nu,x)</entry><entry><action>scaled irregular modified Bessel function of fractional order nu, exp(|x|) K<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Jnu(ν,x)</entry><entry><action>regular cylindrical Bessel function of fractional order ν, J<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Ynu(ν,x)</entry><entry><action>irregular cylindrical Bessel function of fractional order ν, Y<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Inu(ν,x)</entry><entry><action>regular modified Bessel function of fractional order ν, I<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Inus(ν,x)</entry><entry><action>scaled regular modified Bessel function of fractional order ν, exp(-|x|) I<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>Knu(ν,x)</entry><entry><action>irregular modified Bessel function of fractional order ν, K<subscript>ν</subscript>(x)</action></entry></row> +<row><entry>lnKnu(ν,x)</entry><entry><action>logarithm of the irregular modified Bessel function of fractional order ν,ln(K<subscript>ν</subscript>(x))</action></entry></row> +<row><entry>Knus(ν,x)</entry><entry><action>scaled irregular modified Bessel function of fractional order ν, exp(|x|) K<subscript>ν</subscript>(x)</action></entry></row> <row><entry>J0_0(s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>0</subscript>(x)</action></entry></row> <row><entry>J1_0(s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>1</subscript>(x)</action></entry></row> <row><entry>Jnu_0(nu,s)</entry><entry><action>s-th positive zero of the Bessel function J<subscript>ν</subscript>(x)</action></entry></row> @@ -902,19 +902,19 @@ For more information about the functions see the documentation of GSL. <row><entry>beta(a,b)</entry><entry><action>Beta Function, B(a,b) = Γ(a) Γ(b)/Γ(a+b) for a > 0, b > 0</action></entry></row> <row><entry>lnbeta(a,b)</entry><entry><action>logarithm of the Beta Function, log(B(a,b)) for a > 0, b > 0</action></entry></row> <row><entry>betainc(a,b,x)</entry><entry><action>normalize incomplete Beta function B_x(a,b)/B(a,b) for a > 0, b > 0 </action></entry></row> -<row><entry>C1(lambda,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>1</subscript>(x)</action></entry></row> -<row><entry>C2(lambda,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>2</subscript>(x)</action></entry></row> -<row><entry>C3(lambda,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>3</subscript>(x)</action></entry></row> -<row><entry>Cn(n,lambda,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>n</subscript>(x)</action></entry></row> +<row><entry>C1(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>1</subscript>(x)</action></entry></row> +<row><entry>C2(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>2</subscript>(x)</action></entry></row> +<row><entry>C3(λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>3</subscript>(x)</action></entry></row> +<row><entry>Cn(n,λ,x)</entry><entry><action>Gegenbauer polynomial C<superscript>λ</superscript><subscript>n</subscript>(x)</action></entry></row> <row><entry>hyperg_0F1(c,x)</entry><entry><action>hypergeometric function <subscript>0</subscript>F<subscript>1</subscript>(c,x)</action></entry></row> <row><entry>hyperg_1F1i(m,n,x)</entry><entry><action>confluent hypergeometric function <subscript>1</subscript>F<subscript>1</subscript>(m,n,x) = M(m,n,x) for integer parameters m, n</action></entry></row> <row><entry>hyperg_1F1(a,b,x)</entry><entry><action>confluent hypergeometric function <subscript>1</subscript>F<subscript>1</subscript>(a,b,x) = M(a,b,x) for general parameters a,b</action></entry></row> <row><entry>hyperg_Ui(m,n,x)</entry><entry><action>confluent hypergeometric function U(m,n,x) for integer parameters m,n</action></entry></row> <row><entry>hyperg_U(a,b,x)</entry><entry><action>confluent hypergeometric function U(a,b,x)</action></entry></row> <row><entry>hyperg_2F1(a,b,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x)</action></entry></row> -<row><entry>hyperg_2F1c(ar,ai,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) with complex parameters</action></entry></row> -<row><entry>hyperg_2F1r(ar,ai,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x) / Γ(c)</action></entry></row> -<row><entry>hyperg_2F1cr(ar,ai,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) / Γ(c)</action></entry></row> +<row><entry>hyperg_2F1c(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) with complex parameters</action></entry></row> +<row><entry>hyperg_2F1r(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a,b,c,x) / Γ(c)</action></entry></row> +<row><entry>hyperg_2F1cr(a<subscript>R</subscript>,a<subscript>I</subscript>,c,x)</entry><entry><action>renormalized Gauss hypergeometric function <subscript>2</subscript>F<subscript>1</subscript>(a<subscript>R</subscript> + i a<subscript>I</subscript>, a<subscript>R</subscript> - i a<subscript>I</subscript>, c, x) / Γ(c)</action></entry></row> <row><entry>hyperg_2F0(a,b,x)</entry><entry><action>hypergeometric function <subscript>2</subscript>F<subscript>0</subscript>(a,b,x)</action></entry></row> <row><entry>L1(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>1</subscript>(x)</action></entry></row> <row><entry>L2(a,x)</entry><entry><action>generalized Laguerre polynomials L<superscript>a</superscript><subscript>2</subscript>(x)</action></entry></row> @@ -930,15 +930,15 @@ For more information about the functions see the documentation of GSL. <row><entry>Ql(l,x)</entry><entry><action>Legendre polynomials Q<subscript>l</subscript>(x)</action></entry></row> <row><entry>Plm(l,m,x)</entry><entry><action>associated Legendre polynomial P<subscript>l</subscript><superscript>m</superscript>(x)</action></entry></row> <row><entry>Pslm(l,m,x)</entry><entry><action>normalized associated Legendre polynomial √{(2l+1)/(4π)} √{(l-m)!/(l+m)!} P<subscript>l</subscript><superscript>m</superscript>(x) suitable for use in spherical harmonics</action></entry></row> -<row><entry>Phalf(lambda,x)</entry><entry><action>irregular Spherical Conical Function P<superscript>1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Pmhalf(lambda,x)</entry><entry><action>regular Spherical Conical Function P<superscript>-1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Pc0(lambda,x)</entry><entry><action>conical function P<superscript>0</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Pc1(lambda,x)</entry><entry><action>conical function P<superscript>1</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> -<row><entry>Psr(l,lambda,x)</entry><entry><action>Regular Spherical Conical Function P<superscript>-1/2-l</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, l >= -1</action></entry></row> -<row><entry>Pcr(l,lambda,x)</entry><entry><action>Regular Cylindrical Conical Function P<superscript>-m</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, m >= -1</action></entry></row> -<row><entry>H3d0(lambda,eta)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>0</subscript>(lambda,eta) := sin(lambda eta)/(lambda sinh(eta)) for eta >= 0</action></entry></row> -<row><entry>H3d1(lambda,eta)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>1</subscript>(lambda,eta) := 1/√{lambda<superscript>2</superscript> + 1} sin(lambda eta)/(lambda sinh(eta)) (coth(eta) - lambda cot(lambda eta)) for eta >= 0</action></entry></row> -<row><entry>H3d(l,lambda,eta)</entry><entry><action>L'th radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space eta >= 0, l >= 0</action></entry></row> +<row><entry>Phalf(λ,x)</entry><entry><action>irregular Spherical Conical Function P<superscript>1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Pmhalf(λ,x)</entry><entry><action>regular Spherical Conical Function P<superscript>-1/2</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Pc0(λ,x)</entry><entry><action>conical function P<superscript>0</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Pc1(λ,x)</entry><entry><action>conical function P<superscript>1</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1</action></entry></row> +<row><entry>Psr(l,λ,x)</entry><entry><action>Regular Spherical Conical Function P<superscript>-1/2-l</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, l >= -1</action></entry></row> +<row><entry>Pcr(l,λ,x)</entry><entry><action>Regular Cylindrical Conical Function P<superscript>-m</superscript><subscript>-1/2 + i λ</subscript>(x) for x > -1, m >= -1</action></entry></row> +<row><entry>H3d0(λ,η)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>0</subscript>(λ,,η) := sin(λ η)/(λ sinh(η)) for η >= 0</action></entry></row> +<row><entry>H3d1(λ,η)</entry><entry><action>zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L<superscript>H3d</superscript><subscript>1</subscript>(λ,η) := 1/√{λ<superscript>2</superscript> + 1} sin(λ η)/(λ sinh(η)) (coth(η) - λ cot(λ η)) for η >= 0</action></entry></row> +<row><entry>H3d(l,λ,η)</entry><entry><action>L'th radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space eta >= 0, l >= 0</action></entry></row> <row><entry>logabs(x)</entry><entry><action>logarithm of the magnitude of X, log(|x|)</action></entry></row> <row><entry>logp(x)</entry><entry><action>log(1 + x) for x > -1 using an algorithm that is accurate for small x</action></entry></row> <row><entry>logm(x)</entry><entry><action>log(1 + x) - x for x > -1 using an algorithm that is accurate for small x</action></entry></row> @@ -957,14 +957,14 @@ For more information about the functions see the documentation of GSL. <row><entry>sinc(x)</entry><entry><action>sinc(x) = sin(π x) / (π x)</action></entry></row> <row><entry>logsinh(x)</entry><entry><action>log(sinh(x)) for x > 0</action></entry></row> <row><entry>logcosh(x)</entry><entry><action>log(cosh(x))</action></entry></row> -<row><entry>anglesymm(theta)</entry><entry><action>force the angle theta to lie in the range (-π,π]</action></entry></row> -<row><entry>anglepos(theta)</entry><entry><action>force the angle theta to lie in the range (0,2π]</action></entry></row> -<row><entry>zetaint(n)</entry><entry><action>Riemann zeta function zeta(n) for integer n</action></entry></row> -<row><entry>zeta(s)</entry><entry><action>Riemann zeta function zeta(s) for arbitrary s</action></entry></row> -<row><entry>zetam1int(n)</entry><entry><action>Riemann zeta function minus 1 for integer n</action></entry></row> -<row><entry>zetam1(s)</entry><entry><action>Riemann zeta function minus 1</action></entry></row> -<row><entry>zetaintm1(s)</entry><entry><action>Riemann zeta function for integer n minus 1</action></entry></row> -<row><entry>hzeta(s,q)</entry><entry><action>Hurwitz zeta function zeta(s,q) for s > 1, q > 0</action></entry></row> +<row><entry>anglesymm(α)</entry><entry><action>force the angle α to lie in the range (-π,π]</action></entry></row> +<row><entry>anglepos(α)</entry><entry><action>force the angle α to lie in the range (0,2π]</action></entry></row> +<row><entry>zetaint(n)</entry><entry><action>Riemann zeta function ζ(n) for integer n</action></entry></row> +<row><entry>zeta(s)</entry><entry><action>Riemann zeta function ζ(s) for arbitrary s</action></entry></row> +<row><entry>zetam1int(n)</entry><entry><action>Riemann ζ function minus 1 for integer n</action></entry></row> +<row><entry>zetam1(s)</entry><entry><action>Riemann ζ function minus 1</action></entry></row> +<row><entry>zetaintm1(s)</entry><entry><action>Riemann ζ function for integer n minus 1</action></entry></row> +<row><entry>hzeta(s,q)</entry><entry><action>Hurwitz zeta function ζ(s,q) for s > 1, q > 0</action></entry></row> <row><entry>etaint(n)</entry><entry><action>eta function η(n) for integer n</action></entry></row> <row><entry>eta(s)</entry><entry><action>eta function η(s) for arbitrary s</action></entry></row> <row><entry>gsl_log1p(x)</entry><entry><action>log(1+x)</action></entry></row>
