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The method of differentiating under the integral sign

1990
*
Journal of symbolic computation
*

Introduction

doi:10.1016/s0747-7171(08)80159-9
fatcat:dm4rwxvn3fao5cw6gkh5tsogb4
*The**method**of**differentiating**under**the**integral**sign*can be described as follows. ...*The**Method**of*Differencing*under**the**Integral**Sign**The*same idea can be used to find a linear recurrence relation satisfied by where Nan, := an+l. ...*The*same*method**of*proof yields that*under**the*condition*of**the*lemma (P(x, y)/Q(x, y))" is always holonomic, and, since holonomicity is closed*under*multiplication (Zeilberger, to appear) also any product ...##
###
Differentiating under integral sign in Castigliano's theorem

2019
*
Mathematics in Education Research and Applications
*

We showed

doi:10.15414/meraa.2019.05.01.30-37
fatcat:dctemdmh35dbleajp44y54sy4e
*the*derivation*of*modified Castigliano's theorem via Leibnitz rule*of**differentiating**under**integration**sign*. ...*The*Dormand-Prince numerical*integration**method*was used for*the*numerical*integration*. Comparing*the*exact and numerical solution we got*the*error*of*numerical*integration*solution. ...*The**method**of**differentiating**the*functions*under**integral**sign*was analyzed by [1, 5, 8, 14] . ...##
###
Study of Memory Effect in a Fuzzy EOQ Model with No Shortage

2019
*
International Journal of Intelligent Systems and Applications
*

Here,

doi:10.5815/ijisa.2019.11.06
fatcat:o2ttvxmybfbm5idwdjunvr6g5e
*the*fractional order model is defuzzyfied using (i)*signed*distance*method*,(ii) graded mean*integration**method*. ...*The*feature*of**the*fractional order derivative and fractional order*integration*is one*of**the*important tools to realize*the*beauty*of**the*fractional calculus. ...*The*first author would also like to thank*the*Department*of*science and Technology, Government*of*India, New Delhi, for*the*financial assistance*under*AORC, Inspire fellowship Scheme towards this research ...##
###
Some divergent trigonometric integrals
[article]

2001
*
arXiv
*
pre-print

*The*original error was made when a (startlingly) famous mathematician incorrectly

*differentiated*

*under*

*the*

*integral*

*sign*with some convergent

*integrals*that depend on a paramater. ... Some divergent trigonometric

*integrals*have appeared in standard tables for many years, listed as converging. We give a simple proof that these

*integrals*diverge and trace their history. ... But,

*differentiating*

*under*

*the*

*integral*

*sign*leads to our divergent

*integrals*(1). ...

##
###
Some Divergent Trigonometric Integrals

2001
*
The American mathematical monthly
*

He then proceeds to

doi:10.1080/00029890.2001.11919769
fatcat:4qibbtids5c7biyyakuc4nx2qe
*differentiate**under**the**integral**sign*with respect to b. Very bad! ... It gives*the*same incorrect values that are in*the*tables.*DIFFERENTIATION**UNDER**THE**INTEGRAL**SIGN*. ...##
###
Some Divergent Trigonometric Integrals

2001
*
The American mathematical monthly
*

He then proceeds to

doi:10.2307/2695797
fatcat:dznbmbtnirbg3d7pspqvvxaati
*differentiate**under**the**integral**sign*with respect to b. Very bad! ... It gives*the*same incorrect values that are in*the*tables.*DIFFERENTIATION**UNDER**THE**INTEGRAL**SIGN*. ...##
###
A Modified Differential Coherent Bit Synchronization Algorithm for BeiDou Weak Signals with Large Frequency Deviation

2017
*
Sensors
*

*The*results show that

*the*proposed algorithm outperforms

*the*traditional

*method*with a frequency deviation

*of*50 Hz. ... Firstly, a

*differential*coherent approach is used to remove

*the*effect

*of*frequency deviation, and

*the*

*differential*delay time is set to be a multiple

*of*bit cycle to remove

*the*influence

*of*NH code. ... Conflicts

*of*Interest:

*The*authors declare no conflict

*of*interest. ...

##
###
Page 3135 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
*
Mathematical Reviews
*

“In

*the*fifth chapter we discuss*the*application*of**the**method**of**sign*-definite functions to*the*problem*of*stability*of*solutions*of*systems*of**differential*-difference equations. ... This reflects our belief that*the**method**of**sign*-definite functions*of*a finite number*of*variables is a universal tool for*the*study*of**the*stability*of*solutions for systems*of*ordinary*differential*...##
###
Page 145 of Annals of Mathematics Vol. 3, Issue 3
[page]

1902
*
Annals of Mathematics
*

Z | aie arid y /0
converges for all values

*of*a and represents*the*function ¢(@) = @. Can*the**integral*be*differentiated**under**the**sign**of**integration*? and a = 41.*The**integral*42. ... Is it allowable here to*differentiate**under**the**sign**of**integration*for all values*of*a’ If not, and if you bave used*the**method*suggested in Problem 13, have you been careful to make your solution rigorous ...##
###
Numerical time integration of lumped parameter systems governed by implicit constitutive relations
[article]

2017
*
arXiv
*
pre-print

Using this new

arXiv:1711.06352v1
fatcat:txnak6cgwzb47h47za7aeqyiky
*method*,*the*limitations*of**the*trapezoidal time-*integration**methods*when applied to a non-smooth*differential*-algebraic equation are highlighted. ...*Under*this scheme, implicit-explicit*integration**of**the*governing equations is possible. ... A complete description*of*numerical*integration**under**the*proposed*methods*for cases*of*linear and nonlinear Bingham models is given. ...##
###
The Application of Modern Theories of Integration to the Solution of Differential Equations

1921
*
Annals of Mathematics
*

*Differentiation*and

*integration*

*under*

*the*

*sign*

*of*

*integration*. ...

*The*Stieltjes

*integral*, 1(t) = fib f(X)dx(X, t) (27)

*Differentiation*

*under*

*the*

*sign*

*of*

*integration*. ... (b) It is found that an important class

*of*Stieltjes

*integrals*may be

*differentiated*and

*integrated*

*under*

*the*

*sign*

*of*

*integration*, provided that, when

*differentiation*is performed, left-hand unilateral ...

##
###
Integrated Guidance and Control Method for the Interception of Maneuvering Hypersonic Vehicle Based on High Order Sliding Mode Approach

2015
*
Mathematical Problems in Engineering
*

To estimate

doi:10.1155/2015/648231
fatcat:yponx66255fiddk4vp5rvrlame
*the*high order derivatives*of**the*sliding manifold which is required in*the*HOSM*method*, an Arbitrary Order Robust Exact*Differentiator*is presented. ... This paper focuses on*the**integrated*guidance and control (IGC)*method*applied in*the*interception*of*maneuvering near space hypersonic vehicles using*the*homogeneous high order sliding mode (HOSM) approach ... Conflict*of*Interests*The*authors declare that there is no conflict*of*interests regarding*the*publication*of*this paper. ...##
###
The XY

1913
*
Mathematical Gazette
*

An

doi:10.2307/3604373
fatcat:diph4fdxnnexhpzs7r3xtxeriy
*integral*equation is an equation involving*signs**of**integration*just as a*differential*equation involves*signs**of**differentiation*. Thus dy y=l+ xydx is*the*same as d=xy. y=l when x=0. ... An*integral*equation is an equation involving*signs**of**integration*just as a*differential*equation involves*signs**of**differentiation*. Thus dy y=l+ xydx is*the*same as d=xy. y=l when x=0. ...##
###
From Cagniard's method for solving seismic pulse problems to the method of the differential transform

1982
*
Computers and Mathematics with Applications
*

*The*technique

*of*

*the*

*differential*transform, which evolved from that

*of*Cagniard, involves an

*integral*-free transform and avoids

*the*

*integral*considerations associated with Cagniard's technique. ...

*The*

*integral*transform

*method*

*of*Cagniard involves path deformations in

*the*complex plane, residue calculus and, in some cases, branch cuts. ...

*The*crucial point, however, is that it might be difficult or impossible to follow

*the*procedure in Diagram 3.1 if complicated functions A(r), B(T) or C(r) are inserted

*under*

*the*

*integral*

*signs*

*of*(4.3) ...

##
###
Page 112 of Proceedings of the National Academy of Sciences of the United States of America Vol. 18, Issue 1
[page]

1932
*
Proceedings of the National Academy of Sciences of the United States of America
*

ON

*THE*CHANGES*OF**SIGN**OF**THE*DERIVATIVES*OF*A FUNCTION DEFINED BY A LAPLACE*INTEGRAL*By D. V. ...*Under*certain conditions this*method*enables one to complete*the*covariant derivative*of*a tensor J in avery satisfactory manner. ...
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