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Formula:6030

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Digital Library of Mathematical Functions ID 17.2.E43

π’Ÿ q ⁒ ( f ⁒ ( z ) ⁒ g ⁒ ( z ) ) = g ⁒ ( z ) ⁒ f [ 1 ] ⁒ ( z ) + f ⁒ ( z ⁒ q ) ⁒ g [ 1 ] ⁒ ( z ) . subscript π’Ÿ π‘ž 𝑓 𝑧 𝑔 𝑧 𝑔 𝑧 superscript 𝑓 delimited-[] 1 𝑧 𝑓 𝑧 π‘ž superscript 𝑔 delimited-[] 1 𝑧 {\displaystyle{\displaystyle\mathcal{D}_{q}(f(z)g(z))=g(z)f^{[1]}(z)+f(zq)g^{[% 1]}(z).}}


Constraint(s)

Symbols List

  • q π‘ž {\displaystyle{\displaystyle q}} : complex base
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • π’Ÿ q subscript π’Ÿ π‘ž {\displaystyle{\displaystyle\mathcal{D}_{q}}} : $$q$$ -differential operator (locally)
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