Formula:5847

Digital Library of Mathematical Functions ID 15.10.E34

${\displaystyle{\displaystyle w_{1}(z)=e^{(c-b)\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-a\right)}{\Gamma\left(b\right)\Gamma\left(c-a-b+1\right)}w_{4}(z)+e^{-b\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-a\right)}{\Gamma\left(b-a+1\right)\Gamma\left(c-b\right)}w_{6}(z),}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle b}}$: real or complex parameter
• ${\displaystyle{\displaystyle c}}$: real or complex parameter
• ${\displaystyle{\displaystyle w_{m}(z)}}$: Kummer’s solutions
 

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