Transformation formulas
Transformation formulas
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Euler's transformation formula}\index{Transformation formula!Euler} \HyperpFq{2}{1}@@{a,b}{c}{z}=(1-z)^{c-a-b}\,\HyperpFq{2}{1}@@{c-a,c-b}{c}{z} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Pfaff-Kummer transformation formula}\index{Transformation formula!Pfaff-Kummer} \HyperpFq{2}{1}@@{a,b}{c}{z}=(1-z)^{-a}\,\HyperpFq{2}{1}@@{a,c-b}{c}{\frac{z}{z-1}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Kummer's transformation formula}\index{Transformation formula!Kummer} \HyperpFq{1}{1}@@{a}{c}{z}=\expe^z\,\HyperpFq{1}{1}@@{c-a}{c}{-z} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \HyperpFq{1}{1}@@{-n}{a}{x}=\frac{(-x)^n}{\pochhammer{a}{n}}\,\HyperpFq{2}{0}@@{-n,-a-n+1}{-}{-\frac{1}{x}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \HyperpFq{2}{1}@@{-n,b}{c}{x}=\frac{\pochhammer{b}{n}}{\pochhammer{c}{n}}(-x)^n\,\HyperpFq{2}{1}@@{-n,-c-n+1}{-b-n+1}{\frac{1}{x}} }}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \index{Whipple's transformation formula}\index{Transformation formula!Whipple} \HyperpFq{4}{3}@@{-n,a,b,c}{d,e,f}{1} {}=\frac{\pochhammer{e-a}{n}\pochhammer{f-a}{n}}{\pochhammer{e}{n}\pochhammer{f}{n}}\HyperpFq{4}{3}@@{-n,a,d-b,d-c}{d,a-e-n+1,a-f-n+1}{1} }}