@@ Property / constraint @@
+ ${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}$ 
|\phase@@{z}|\leq\tfrac{1}{2}\pi-\delta
+Normal rank
@@ Property / Symbols used @@
+order not exceeding
@@ Property / Symbols used: order not exceeding / rank @@
+Normal rank
@@ Property / Symbols used: order not exceeding / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$ 
\bigO@{\NVar{x}}
@@ Property / Symbols used: order not exceeding / qualifier @@
+xml-id: C2.S1.E3.m2adec
@@ 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 @@
+base of natural logarithm
@@ Property / Symbols used: base of natural logarithm / rank @@
+Normal rank
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2afdec
@@ Property / Symbols used @@
+modified Bessel function of the first kind
@@ Property / Symbols used: modified Bessel function of the first kind / rank @@
+Normal rank
@@ Property / Symbols used: modified Bessel function of the first kind / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\modBesselI{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: modified Bessel function of the first kind / qualifier @@
+xml-id: C10.S25.E2.m2acdec
@@ 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.m1adec
@@ Property / Symbols used @@
+Q11428
@@ Property / Symbols used: Q11428 / rank @@
+Normal rank
@@ Property / Symbols used: Q11428 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle k}}$ 
k
@@ Property / Symbols used: Q11428 / qualifier @@
+xml-id: C10.S1.XMD3.m1fdec
@@ Property / Symbols used @@
+Q11426
@@ Property / Symbols used: Q11426 / rank @@
+Normal rank
@@ Property / Symbols used: Q11426 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11426 / qualifier @@
+xml-id: C10.S1.XMD6.m1idec
@@ Property / Symbols used @@
+Q11427
@@ Property / Symbols used: Q11427 / rank @@
+Normal rank
@@ Property / Symbols used: Q11427 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q11427 / qualifier @@
+xml-id: C10.S1.XMD7.m1fdec
@@ Property / Symbols used @@
+Q11442
@@ Property / Symbols used: Q11442 / rank @@
+Normal rank
@@ Property / Symbols used: Q11442 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\delta}}$ 
\delta
@@ Property / Symbols used: Q11442 / qualifier @@
+xml-id: C10.S1.XMD8.m1dec
@@ Property / Symbols used @@
+DLMF:10.41.E7
@@ Property / Symbols used: DLMF:10.41.E7 / rank @@
+Normal rank
@@ Property / Symbols used: DLMF:10.41.E7 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\eta}}$ 
\eta
@@ Property / Symbols used: DLMF:10.41.E7 / qualifier @@
+xml-id: C10.S41.XMD1.m1fdec
@@ Property / Symbols used @@
+Q11480
@@ Property / Symbols used: Q11480 / rank @@
+Normal rank
@@ Property / Symbols used: Q11480 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle p}}$ 
p
@@ Property / Symbols used: Q11480 / qualifier @@
+xml-id: C10.S41.XMD2.m1dec
@@ Property / Symbols used @@
+Q11453
@@ Property / Symbols used: Q11453 / rank @@
+Normal rank
@@ Property / Symbols used: Q11453 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle U_{k}(p)}}$ 
U_{k}(p)
@@ Property / Symbols used: Q11453 / qualifier @@
+xml-id: C10.S41.XMD3.m1ddec

DLMF:10.41.E12 (Q3609): Difference between revisions

| ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

π {\displaystyle{\displaystyle\pi}}

e {\displaystyle{\displaystyle\mathrm{e}}}

I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

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

k 𝑘 {\displaystyle{\displaystyle k}}

z 𝑧 {\displaystyle{\displaystyle z}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

δ 𝛿 {\displaystyle{\displaystyle\delta}}

η 𝜂 {\displaystyle{\displaystyle\eta}}

p 𝑝 {\displaystyle{\displaystyle p}}

U k ⁢ ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}}

Latest revision as of 13:57, 2 January 2020

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${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}$

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

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

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$

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

${\displaystyle{\displaystyle k}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle\nu}}$

${\displaystyle{\displaystyle\delta}}$

${\displaystyle{\displaystyle\eta}}$

${\displaystyle{\displaystyle p}}$

${\displaystyle{\displaystyle U_{k}(p)}}$