@@ Property / constraint @@
+ ${\displaystyle{\displaystyle|z|<1}}$ 
|z|<1
@@ Property / constraint: ${\displaystyle{\displaystyle|z|<1}}$ / rank @@
+Normal rank
@@ Property / Symbols used @@
+Q11581
@@ Property / Symbols used: Q11581 / rank @@
+Normal rank
@@ Property / Symbols used: Q11581 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}$ 
\genhyperF{2}{1}@{\NVar{a},\NVar{b}}{\NVar{c}}{\NVar{z}}
@@ Property / Symbols used: Q11581 / qualifier @@
+xml-id: C16.S2.m5adec
@@ Property / Symbols used @@
+Q11660
@@ Property / Symbols used: Q11660 / rank @@
+Normal rank
@@ Property / Symbols used: Q11660 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}$ 
\JacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}
@@ Property / Symbols used: Q11660 / qualifier @@
+xml-id: C18.S3.T1.t1.r2.m2abdec
@@ Property / Symbols used @@
+Q10759
@@ Property / Symbols used: Q10759 / rank @@
+Normal rank
@@ Property / Symbols used: Q10759 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$ 
\Pochhammersym{\NVar{a}}{\NVar{n}}
@@ Property / Symbols used: Q10759 / qualifier @@
+xml-id: C5.S2.SS3.m1adec
@@ Property / Symbols used @@
+Q11750
@@ Property / Symbols used: Q11750 / rank @@
+Normal rank
@@ Property / Symbols used: Q11750 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11750 / qualifier @@
+xml-id: C18.S1.XMD2.m1bdec
@@ Property / Symbols used @@
+Q11726
@@ Property / Symbols used: Q11726 / rank @@
+Normal rank
@@ Property / Symbols used: Q11726 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle n}}$ 
n
@@ Property / Symbols used: Q11726 / qualifier @@
+xml-id: C18.S1.XMD6.m1bdec
@@ Property / Symbols used @@
+Q11727
@@ Property / Symbols used: Q11727 / rank @@
+Normal rank
@@ Property / Symbols used: Q11727 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q11727 / qualifier @@
+xml-id: C18.S2.XMD3.m1bdec

DLMF:18.12.E3 (Q5645): Difference between revisions

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

z 𝑧 {\displaystyle{\displaystyle z}}

n 𝑛 {\displaystyle{\displaystyle n}}

x 𝑥 {\displaystyle{\displaystyle x}}

Latest revision as of 15:31, 2 January 2020

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${\displaystyle{\displaystyle|z|<1}}$

${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}$

${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}$

${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle x}}$