@@ Property / constraint @@
+ ${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}$ 
|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta
+Normal rank
@@ Property / Symbols used @@
+Q10931
@@ Property / Symbols used: Q10931 / rank @@
+Normal rank
@@ Property / Symbols used: Q10931 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\sim}}$ 
\asympexp
@@ Property / Symbols used: Q10931 / qualifier @@
+xml-id: C2.S1.SS3.p1.m11aadec
@@ 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.m2acdec
@@ 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.m2addec
@@ Property / Symbols used @@
+incomplete gamma function
@@ Property / Symbols used: incomplete gamma function / rank @@
+Normal rank
@@ Property / Symbols used: incomplete gamma function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}$ 
\incGamma@{\NVar{a}}{\NVar{z}}
@@ Property / Symbols used: incomplete gamma function / qualifier @@
+xml-id: C8.S2.E2.m2aadec
@@ 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.m1acdec
@@ Property / Symbols used @@
+Q11332
@@ Property / Symbols used: Q11332 / rank @@
+Normal rank
@@ Property / Symbols used: Q11332 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q11332 / qualifier @@
+xml-id: C8.S1.XMD1.m1adec
@@ Property / Symbols used @@
+Q11323
@@ Property / Symbols used: Q11323 / rank @@
+Normal rank
@@ Property / Symbols used: Q11323 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11323 / qualifier @@
+xml-id: C8.S1.XMD2.m1edec
@@ Property / Symbols used @@
+Q11324
@@ Property / Symbols used: Q11324 / rank @@
+Normal rank
@@ Property / Symbols used: Q11324 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle a}}$ 
a
@@ Property / Symbols used: Q11324 / qualifier @@
+xml-id: C8.S1.XMD3.m1fdec
@@ Property / Symbols used @@
+Q11330
@@ Property / Symbols used: Q11330 / rank @@
+Normal rank
@@ Property / Symbols used: Q11330 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle k}}$ 
k
@@ Property / Symbols used: Q11330 / qualifier @@
+xml-id: C8.S1.XMD5.m1ddec
@@ Property / Symbols used @@
+Q11343
@@ Property / Symbols used: Q11343 / rank @@
+Normal rank
@@ Property / Symbols used: Q11343 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\delta}}$ 
\delta
@@ Property / Symbols used: Q11343 / qualifier @@
+xml-id: C8.S1.XMD7.m1cdec
@@ Property / Symbols used @@
+Q11344
@@ Property / Symbols used: Q11344 / rank @@
+Normal rank
@@ Property / Symbols used: Q11344 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\lambda}}$ 
\lambda
@@ Property / Symbols used: Q11344 / qualifier @@
+xml-id: C8.S11.XMD3.m1adec
@@ Property / Symbols used @@
+Q11345
@@ Property / Symbols used: Q11345 / rank @@
+Normal rank
@@ Property / Symbols used: Q11345 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle b_{k}(\lambda)}}$ 
b_{k}(\lambda)
@@ Property / Symbols used: Q11345 / qualifier @@
+xml-id: C8.S11.XMD4.m1adec

DLMF:8.11.E7 (Q2578): Difference between revisions

| ph ⁡ a | ≤ 3 ⁢ π 2 - δ ph 𝑎 3 𝜋 2 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

π {\displaystyle{\displaystyle\pi}}

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

Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}

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

x 𝑥 {\displaystyle{\displaystyle x}}

z 𝑧 {\displaystyle{\displaystyle z}}

a 𝑎 {\displaystyle{\displaystyle a}}

k 𝑘 {\displaystyle{\displaystyle k}}

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

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

b k ⁢ ( λ ) subscript 𝑏 𝑘 𝜆 {\displaystyle{\displaystyle b_{k}(\lambda)}}

Latest revision as of 13:54, 2 January 2020

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${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}$

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

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

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

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

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

${\displaystyle{\displaystyle x}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle a}}$

${\displaystyle{\displaystyle k}}$

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

${\displaystyle{\displaystyle\lambda}}$

${\displaystyle{\displaystyle b_{k}(\lambda)}}$