@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}$ 
\abs{\phase@@{z}}\leq\frac{1}{2}\pi-\delta
+Normal rank
@@ Property / Symbols used @@
+gamma function
@@ Property / Symbols used: gamma function / rank @@
+Normal rank
@@ Property / Symbols used: gamma function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 
\EulerGamma@{\NVar{z}}
@@ Property / Symbols used: gamma function / qualifier @@
+xml-id: C5.S2.E1.m2ahdec
@@ Property / Symbols used @@
+Whittaker confluent hypergeometric function
@@ Property / Symbols used: Whittaker confluent hypergeometric function / rank @@
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ 
\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
+xml-id: C13.S14.E2.m2ahdec
@@ 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.m2addec
@@ 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.m2aldec
@@ 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 @@
+Q11557
@@ Property / Symbols used: Q11557 / rank @@
+Normal rank
@@ Property / Symbols used: Q11557 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11557 / qualifier @@
+xml-id: C13.S1.XMD6.m1sdec
@@ Property / Symbols used @@
+Q11560
@@ Property / Symbols used: Q11560 / rank @@
+Normal rank
@@ Property / Symbols used: Q11560 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\delta}}$ 
\delta
@@ Property / Symbols used: Q11560 / qualifier @@
+xml-id: C13.S1.XMD7.m1dec
@@ Property / Symbols used @@
+asymptotic equality
@@ Property / Symbols used: asymptotic equality / rank @@
+Normal rank
@@ Property / Symbols used: asymptotic equality / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\sim}}$ 
\asympeq
@@ Property / Symbols used: asymptotic equality / qualifier @@
+xml-id: C2.S1.E1.m2adec

DLMF:13.14.E20 (Q4509): Difference between revisions

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

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

π {\displaystyle{\displaystyle\pi}}

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

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

z 𝑧 {\displaystyle{\displaystyle z}}

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

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

Latest revision as of 16:06, 2 January 2020

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${\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}$

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$

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

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

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

${\displaystyle{\displaystyle z}}$

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

${\displaystyle{\displaystyle\sim}}$