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Formula:9538

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Digital Library of Mathematical Functions ID 30.4.E2

π–―π—Œ n m ⁑ ( x , 0 ) = 𝖯 n m ⁑ ( x ) ; spheroidal-wave-on-cut-Ps π‘š 𝑛 π‘₯ 0 Ferrers-Legendre-P-first-kind π‘š 𝑛 π‘₯ {\displaystyle{\displaystyle\mathsf{Ps}^{m}_{n}\left(x,0\right)=\mathsf{P}^{m}% _{n}\left(x\right);}}


Constraint(s)

Symbols List

  • 𝖯 Ξ½ ΞΌ ⁑ ( x ) Ferrers-Legendre-P-first-kind πœ‡ 𝜈 π‘₯ {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}} : Ferrers function of the first kind
  • π–―π—Œ n m ⁑ ( x , Ξ³ 2 ) spheroidal-wave-on-cut-Ps π‘š 𝑛 π‘₯ superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}} :
  • x π‘₯ {\displaystyle{\displaystyle x}} : real variable
  • m π‘š {\displaystyle{\displaystyle m}} : nonnegative integer
  • n β‰₯ m 𝑛 π‘š {\displaystyle{\displaystyle n\geq m}} : integer degree
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This page was last edited on 28 January 2024, at 10:02.
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