@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}$ 
\abs{\phase@{-z}}<\pi
+Normal rank
@@ Property / Symbols used @@
+Q11481
@@ Property / Symbols used: Q11481 / rank @@
+Normal rank
@@ Property / Symbols used: Q11481 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: Q11481 / qualifier @@
+xml-id: C14.S21.SS1.p1.m1aedec
@@ Property / Symbols used @@
+the ratio of the circumference of a circle to its diameter
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\pi}}$ 
\cpi
+xml-id: C3.S12.E1.m2afdec
@@ Property / Symbols used @@
+Q10817
@@ Property / Symbols used: Q10817 / rank @@
+Normal rank
@@ Property / Symbols used: Q10817 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{ph}}}$ 
\phase
@@ Property / Symbols used: Q10817 / qualifier @@
+xml-id: C1.S9.E7.m1aedec
@@ Property / Symbols used @@
+$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$  Olver’s hypergeometric function
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}$ 
\hyperOlverF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
+xml-id: C15.S2.E2.m2aedec
@@ Property / Symbols used @@
+Q11644
@@ Property / Symbols used: Q11644 / rank @@
+Normal rank
@@ Property / Symbols used: Q11644 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11644 / qualifier @@
+xml-id: C15.S1.XMD3.m1fdec
@@ Property / Symbols used @@
+Q11645
@@ Property / Symbols used: Q11645 / rank @@
+Normal rank
@@ Property / Symbols used: Q11645 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle a}}$ 
a
@@ Property / Symbols used: Q11645 / qualifier @@
+xml-id: C15.S1.XMD4.m1edec
@@ Property / Symbols used @@
+Q11647
@@ Property / Symbols used: Q11647 / rank @@
+Normal rank
@@ Property / Symbols used: Q11647 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle c}}$ 
c
@@ Property / Symbols used: Q11647 / qualifier @@
+xml-id: C15.S1.XMD6.m1bdec

DLMF:15.9.E21 (Q5111): Difference between revisions

| ph ⁡ ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

π {\displaystyle{\displaystyle\pi}}

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

𝐅 ⁡ ( a , b ; c ; z ) scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

z 𝑧 {\displaystyle{\displaystyle z}}

a 𝑎 {\displaystyle{\displaystyle a}}

c 𝑐 {\displaystyle{\displaystyle c}}

Latest revision as of 14:11, 2 January 2020

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${\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}$

${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle\pi}}$

${\displaystyle{\displaystyle\operatorname{ph}}}$

${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle a}}$

${\displaystyle{\displaystyle c}}$