Useful expressions of the derivatives, to any order, of Pochhammer and reciprocal Pochhammer symbols with respect to their arguments are presented. They are building blocks of a procedure, recently suggested, for obtaining the ɛ-expansion of functions of the hypergeometric class related to Feynman integrals. The procedure is applied to some examples of such kind of functions taken from the literature.

1.
F.
Jegerlehner
,
M. Yu.
Kalmykov
, and
O.
Veretin
,
Nucl. Phys. B
658
,
49
(
2003
).
2.
A. I.
Davydychev
and
M. Yu.
Kalmykov
,
Nucl. Phys. B
699
,
3
(
2004
).
3.
M. Yu.
Kalmykov
,
J. High Energy Phys.
04
,
056
(
2006
).
4.
M. Yu.
Kalmykov
,
B. F. L.
Ward
, and
S.
Yost
,
J. High Energy Phys.
02
,
040
(
2007
).
5.
M. Yu.
Kalmykov
,
B. F. L.
Ward
, and
S.
Yost
,
J. High Energy Phys.
11
,
009
(
2007
).
6.
M. Yu.
Kalmykov
and
B. A.
Kniehl
,
Phys. Part. Nucl.
41
,
942
(
2010
).
7.
S. A.
Yost
,
V. V.
Bytev
,
M. Yu.
Kalmykov
,
B. A.
Kniehl
, and
B. F. L.
Ward
, “
The epsilon expansion of Feynman diagrams via hypergeometric functions and differential reduction
,” in
Proceedings of the DPF-2011 Conference
,
Providence, RI
, 8–13 August
2011
; e-print arXiv:1110.0210.
8.
S.
Moch
,
P.
Uwer
, and
S.
Weinzierl
,
J. Math. Phys.
43
,
3363
(
2002
).
9.
S.
Weinzierl
,
J. Math. Phys.
45
,
2656
(
2004
).
10.
S.
Weinzierl
,
Comput. Phys. Commun.
145
,
357
(
2002
).
11.
S.
Moch
and
P.
Uwer
,
Comput. Phys. Commun.
174
,
759
(
2006
).
12.
T.
Huber
and
D.
Maître
,
Comput. Phys. Commun.
175
,
122
(
2006
).
13.
T.
Huber
and
D.
Maître
,
Comput. Phys. Commun.
178
,
755
(
2008
).
14.
Z. W.
Huang
and
J.
Liu
,
Comput. Phys. Commun.
184
,
1973
(
2013
).
15.
V. V.
Bytev
,
M. Yu.
Kalmykov
, and
B. A.
Kniehl
,
Comput. Phys. Commun.
184
,
2332
(
2013
).
16.
D.
Greynat
and
J.
Sesma
,
Comput. Phys. Commun.
185
,
472
(
2014
).
17.
L. U.
Ancarani
and
G.
Gasaneo
,
J. Math. Phys.
49
,
063508
(
2008
);
L. U.
Ancarani
and
G.
Gasaneo
,
J. Phys. A: Math. Theor.
42
,
395208
(
2009
);
L. U.
Ancarani
and
G.
Gasaneo
,
J. Phys. A: Math. Theor.
43
,
085210
(
2010
).
18.
V.
Del Duca
,
C.
Duhr
,
E. W. N.
Glover
, and
V. A.
Smirnov
,
J. High Energy Phys.
01
(
2010
)
042
.
19.
20.
Y. L.
Luke
,
The Special Functions and Their Approximations
(
Academic Press
,
New York
,
1969
), Vol.
I
.
21.
NIST Handbook of Mathematical Functions
, edited by
F. W. J.
Olver
,
D. W.
Lozier
,
R. F.
Boisvert
, and
C. W.
Clark
(
Cambridge University Press
,
New York
,
2010
), see free on-line access at http://dlmf.nist.gov.
22.
M. W.
Coffey
, “
Series representations for the Stieltjes constants
,” e-print arXiv:0905.1111.
23.
M. W.
Coffey
, “
Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
,” e-print arXiv:1106.5146.
24.
H. M.
Srivastava
and
P. G.
Todorov
,
J. Math. Anal. Appl.
130
,
509
(
1988
).
25.
Yu. A.
Brychkov
,
Integral Transforms Spec. Funct.
23
,
723
(
2012
).
26.
J.
Vermaseren
,
Int. J. Mod. Phys. A
14
,
2037
(
1999
).
27.
A. P.
Prudnikov
,
Yu. A.
Brychkov
, and
O. I.
Marichev
,
Integrals and Series
(
Gordon and Breach
,
New York
,
1990
), Vol 1.
28.
L.
Comtet
,
Advanced Combinatorics
(
D. Reidel
,
Dordrecht
,
1974
).
29.
J.
Riordan
,
Combinatorial Identities
(
John Wiley & Sons
,
New York
,
1968
).
30.
H. W.
Gould
,
Fibonacci Q.
28
,
166
(
1990
).
31.
P.
Flajolet
and
L. B.
Richmond
,
Random Struct. Algorithms
3
,
305
(
1992
).
32.
P.
Haukkanen
,
Fibonacci Q.
31
,
28
(
1993
).
33.
H.
Prodinger
,
Fibonacci Q.
32
,
412
(
1994
).
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