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- W4285154489 abstract "Abstract In this chapter, we introduce and investigate the map, denote it by Σ, that carries any function g lying in $$displaystyle bigcup _{pgeq 0}(mathcal {D}^pcap mathcal {K}^p) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mrow> <mml:mo>⋃</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:mo>∩</mml:mo> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:math> into the unique solution f to the equation Δ f = g that arises from the existence Theorem 10.1007/978-3-030-95088-0_3#FPar6 . We call these solutions multiple $$log Gamma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>log</mml:mo> <mml:mi>Γ</mml:mi> </mml:math> - type functions and we investigate certain of their properties. We also discuss the search for simple conditions on the function $$gcolon mathbb {R}_+to mathbb {R}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>g</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mrow> <mml:mi>ℝ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>ℝ</mml:mi> </mml:math> to ensure the existence of Σ g . Further important properties of these functions, including counterparts of several classical properties of the gamma function, will be investigated in the next three chapters." @default.
- W4285154489 created "2022-07-14" @default.
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- W4285154489 date "2022-01-01" @default.
- W4285154489 modified "2023-10-18" @default.
- W4285154489 title "Multiple $$log Gamma $$ -Type Functions" @default.
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- W4285154489 doi "https://doi.org/10.1007/978-3-030-95088-0_5" @default.
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