Definition:f
The LaTeX DLMF and DRMF macro \f represents Function.
This macro is in the category of polynomials.
In math mode, this macro can be called in the following ways:
- \f{f} produces Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \f{f}}}
- \f{f}@{x} produces Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \f{f}@{x}}}
These are defined by
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \GenGegenbauer{\alpha}{\beta}{2m}@{x}:={\rm const}\times \Jacobi{\alpha}{\beta}{m}@{2x^2-1}, }
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \GenGegenbauer{\alpha}{\beta}{2m+1}@{x}:={\rm const}\times x\,\Jacobi{\alpha}{\beta+1}{m}@{2x^2-1}. }
Then for Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha,\beta>-1}
, we have the orthogonality relation
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-1}^1 \GenGegenbauer{\alpha}{\beta}{m}@{x}\,\GenGegenbauer{\alpha}{\beta}{n}@{x}\,|x|^{2\beta+1} (1-x^2)^\alpha\,dx=0, }
for Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m\ne n} .
Symbols List
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {f}}}
: function : http://drmf.wmflabs.org/wiki/Definition:f
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle S^{(\alpha,\beta)}_{n}}}
: Generalized Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:GenGegenbauer
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P^{(\alpha,\beta)}_{n}}}
: Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}
: integral : http://dlmf.nist.gov/1.4#iv