一比一仿利兹大学文凭毕业证〖办证V信ATV1819〗adri

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1: Adri B. Olde Daalhuis

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Adri B. Olde Daalhuis

… ►Adri Olde Daalhuis (b. …

2: 11 Struve and Related Functions

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3: 13 Confluent Hypergeometric Functions

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4: 15 Hypergeometric Function

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5: 16 Generalized Hypergeometric Functions & Meijer G-Function

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6: 10 Bessel Functions

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7: Staff

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Adri B. Olde Daalhuis, Mathematics Editor, The University of Edinburgh

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Adri B. Olde Daalhuis, University of Edinburgh, Chaps. 13, 15, 16

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Adri B. Olde Daalhuis, The University of Edinburgh, for Chaps. 13, 15, 16

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8: About the Project

… ►It was fortunate that the project had already recruited Adri Olde Daalhuis from the University of Edinburgh in 2012 to serve as an additional Mathematics Editor. …

9: Preface

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Adri B. Olde Daalhuis, The University of Edinburgh

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10: Errata

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13.2.7 $$U(-m,b,z)={(-1)}^m{\left(b\right)}_{m}M(-m,b,z)={(-1)}^m\sum _{s=0}^m\left(\genfrac{}{}{0.0pt}{}{m}{s}\right){\left(b+s\right)}_{m-s}{(-z)}^s$$

The equality $U(-m,b,z)={(-1)}^m{\left(b\right)}_{m}M(-m,b,z)$ has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Note also that the notation $a=-n$ has been changed to $a=-m$.

Reported 2015-02-10 by Adri Olde Daalhuis.

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13.2.8 $$U(a,a+n+1,z)=\frac{{(-1)}^n{\left(1-a-n\right)}_n}{z^{a+n}}M(-n,1-a-n,z)=z^{-a}\sum _{s=0}^n\left(\genfrac{}{}{0.0pt}{}{n}{s}\right){\left(a\right)}_s{z}^{-s}$$

The equality $U(a,a+n+1,z)=\frac{{(-1)}^n{\left(1-a-n\right)}_n}{z^{a+n}}M(-n,1-a-n,z)$ has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation.

Reported 2015-02-10 by Adri Olde Daalhuis.

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13.2.10 $$U(-m,n+1,z)={(-1)}^m{\left(n+1\right)}_{m}M(-m,n+1,z)={(-1)}^m\sum _{s=0}^m\left(\genfrac{}{}{0.0pt}{}{m}{s}\right){\left(n+s+1\right)}_{m-s}{(-z)}^s$$

The equality $U(-m,n+1,z)={(-1)}^m{\left(n+1\right)}_{m}M(-m,n+1,z)$ has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Note also that the notation $a=-m,m=0,1,2,\mathrm{\dots }$ has been introduced.

Reported 2015-02-10 by Adri Olde Daalhuis.

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On August 24, 2012 Dr. Adri B. Olde Daalhuis was added as Mathematics Editor. This addition has been recorded at the end of the Preface.

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