@@ Property / Symbols used @@
+Q12299
@@ Property / Symbols used: Q12299 / rank @@
+Normal rank
@@ Property / Symbols used: Q12299 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}$ 
\Mathieume{\NVar{n}}@{\NVar{z}}{\NVar{q}}
@@ Property / Symbols used: Q12299 / qualifier @@
+xml-id: C28.S12.SS2.p2.m2aadec
@@ Property / Symbols used @@
+hyperbolic cosine function
@@ Property / Symbols used: hyperbolic cosine function / rank @@
+Normal rank
@@ Property / Symbols used: hyperbolic cosine function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ 
\cosh@@{\NVar{z}}
@@ Property / Symbols used: hyperbolic cosine function / qualifier @@
+xml-id: C4.S28.E2.m2aadec
@@ Property / Symbols used @@
+hyperbolic tangent function
@@ Property / Symbols used: hyperbolic tangent function / rank @@
+Normal rank
@@ Property / Symbols used: hyperbolic tangent function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\tanh\NVar{z}}}$ 
\tanh@@{\NVar{z}}
@@ Property / Symbols used: hyperbolic tangent function / qualifier @@
+xml-id: C4.S28.E4.m2adec
@@ Property / Symbols used @@
+imaginary unit
@@ Property / Symbols used: imaginary unit / rank @@
+Normal rank
@@ Property / Symbols used: imaginary unit / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{i}}}$ 
\iunit
@@ Property / Symbols used: imaginary unit / qualifier @@
+xml-id: C1.S9.E1.m2adec
@@ Property / Symbols used @@
+Q12301
@@ Property / Symbols used: Q12301 / rank @@
+Normal rank
@@ Property / Symbols used: Q12301 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}$ 
\modMathieuM{\NVar{j}}{\NVar{\nu}}@{\NVar{z}}{\NVar{h}}
@@ Property / Symbols used: Q12301 / qualifier @@
+xml-id: C28.S20.SS3.p1.m4aadec
@@ Property / Symbols used @@
+Q12294
@@ Property / Symbols used: Q12294 / rank @@
+Normal rank
@@ Property / Symbols used: Q12294 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle h}}$ 
h
@@ Property / Symbols used: Q12294 / qualifier @@
+xml-id: C28.S1.XMD11.m1adec
@@ Property / Symbols used @@
+Q12279
@@ Property / Symbols used: Q12279 / rank @@
+Normal rank
@@ Property / Symbols used: Q12279 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle n}}$ 
n
@@ Property / Symbols used: Q12279 / qualifier @@
+xml-id: C28.S1.XMD2.m1adec
@@ Property / Symbols used @@
+Q12291
@@ Property / Symbols used: Q12291 / rank @@
+Normal rank
@@ Property / Symbols used: Q12291 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle j}}$ 
j
@@ Property / Symbols used: Q12291 / qualifier @@
+xml-id: C28.S1.XMD3.m1bdec
@@ Property / Symbols used @@
+Q12272
@@ Property / Symbols used: Q12272 / rank @@
+Normal rank
@@ Property / Symbols used: Q12272 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q12272 / qualifier @@
+xml-id: C28.S1.XMD6.m1adec
@@ Property / Symbols used @@
+Q12278
@@ Property / Symbols used: Q12278 / rank @@
+Normal rank
@@ Property / Symbols used: Q12278 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q12278 / qualifier @@
+xml-id: C28.S1.XMD7.m1adec
@@ Property / Symbols used @@
+Q12300
@@ Property / Symbols used: Q12300 / rank @@
+Normal rank
@@ Property / Symbols used: Q12300 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle c_{2m}(q)}}$ 
c_{2m}(q)
@@ Property / Symbols used: Q12300 / qualifier @@
+xml-id: C28.S14.XMD1.m1adec
@@ Property / Symbols used @@
+Q12304
@@ Property / Symbols used: Q12304 / rank @@
+Normal rank
@@ Property / Symbols used: Q12304 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}$ 
\mathcal{C}_{\mu}^{(j)}
@@ Property / Symbols used: Q12304 / qualifier @@
+xml-id: C28.S23.XMD1.m1bdec

DLMF:28.23.E3 (Q8387): Difference between revisions

me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

M ν ( j ) ⁡ ( z , h ) modified-Mathieu-M 𝑗 𝜈 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}

h ℎ {\displaystyle{\displaystyle h}}

n 𝑛 {\displaystyle{\displaystyle n}}

j 𝑗 {\displaystyle{\displaystyle j}}

z 𝑧 {\displaystyle{\displaystyle z}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}

𝒞 μ ( j ) superscript subscript 𝒞 𝜇 𝑗 {\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}

Latest revision as of 15:06, 2 January 2020

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${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}$

${\displaystyle{\displaystyle\cosh\NVar{z}}}$

${\displaystyle{\displaystyle\tanh\NVar{z}}}$

${\displaystyle{\displaystyle\mathrm{i}}}$

${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}$

${\displaystyle{\displaystyle h}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle j}}$

${\displaystyle{\displaystyle z}}$

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

${\displaystyle{\displaystyle c_{2m}(q)}}$

${\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}$