Mathematics | Cambridge Core

Welcome to the mathematics research hub for papers categorised under MSC 2010 classifications as Special Functions. Papers on this page are organised in collections from 33- through 33F, although not all collections may have papers published in that area at this time. Visit the MSC2010 database from MathScinet for a full list of codes.

Jump to the following areas

33-XX: Special functions 33Bxx: Elementary classical functions 33Cxx: Hypergeometric functions 33Dxx: Basic hypergeometric functions 33Exx :Other special functions 33Fxx Computational aspects

Article
A DYNAMICAL SYSTEM PROOF OF NIVEN’S THEOREM AND ITS EXTENSIONS
CHATCHAWAN PANRAKSA, DETCHAT SAMART, SONGPON SRIWONGSA
Bulletin of the Australian Mathematical Society, Volume 109, Issue 1

Article
On two congruence conjectures of Z.-W. Sun involving Franel numbers
Guo-Shuai Mao, Yan Liu
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, First View

Article
On the distribution of the digits of quotients of integers and primes
Alessandro Gambini, Remis Tonon, Alessandro Zaccagnini
Canadian Mathematical Bulletin, Volume 65, Issue 2

Article
Cotangent Sums Related to the Riemann Hypothesis for Various Shifts of the Argument
Helmut Maier, Michael Th. Rassias
Canadian Mathematical Bulletin, Volume 63, Issue 3

Article
SYMMETRIC FUNCTIONS AND MULTIPLE ZETA VALUES
WENCHANG CHU
Bulletin of the Australian Mathematical Society, Volume 101, Issue 3

Article
ON THE ACCURACY OF ASYMPTOTIC APPROXIMATIONS TO THE LOG-GAMMA AND RIEMANN–SIEGEL THETA FUNCTIONS
RICHARD P. BRENT
Journal of the Australian Mathematical Society, Volume 107, Issue 3

Article
SUPERCONGRUENCES INVOLVING $p$-ADIC GAMMA FUNCTIONS
JI-CAI LIU
Bulletin of the Australian Mathematical Society, Volume 98, Issue 1

Article
INEQUALITIES ASSOCIATED WITH RATIOS OF GAMMA FUNCTIONS
JENICA CRINGANU
Bulletin of the Australian Mathematical Society, Volume 97, Issue 3

Article
NEW CONGRUENCES FOR THE TRUNCATED APPELL SERIES $F_1$
XIAOXIA WANG, WENJIE YU
Bulletin of the Australian Mathematical Society, First View

Article
New mock theta functions and formulas for basic hypergeometric series
Olivia X. M. Yao
Proceedings of the Edinburgh Mathematical Society, Volume 66, Issue 3

Article
A $\boldsymbol {q}$ -SUPERCONGRUENCE MODULO THE THIRD POWER OF A CYCLOTOMIC POLYNOMIAL
CHUANAN WEI
Bulletin of the Australian Mathematical Society, Volume 106, Issue 2

Article
A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES $\boldsymbol F_3$
XIAOXIA WANG, MENGLIN YU
Bulletin of the Australian Mathematical Society, Volume 107, Issue 2

Article
A NEW $\boldsymbol {q}$ -ANALOGUE OF VAN HAMME’S (A.2) SUPERCONGRUENCE
VICTOR J. W. GUO
Bulletin of the Australian Mathematical Society, Volume 107, Issue 1

Article
NEW GENERALISATIONS OF VAN HAMME’S (G.2) SUPERCONGRUENCE
NA TANG
Bulletin of the Australian Mathematical Society, Volume 107, Issue 2

Article
A FAMILY OF $\boldsymbol {q}$ -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL
VICTOR J. W. GUO, MICHAEL J. SCHLOSSER
Bulletin of the Australian Mathematical Society, Volume 105, Issue 2

Article
Inverse K-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Takafumi Kouno, Satoshi Naito, Daniel Orr, Daisuke Sagaki
Forum of Mathematics, Sigma, Volume 9

Article
GHOSTS AND CONGRUENCES FOR $\boldsymbol {p}^{\boldsymbol {s}}$-APPROXIMATIONS OF HYPERGEOMETRIC PERIODS
ALEXANDER VARCHENKO, WADIM ZUDILIN
Journal of the Australian Mathematical Society, Volume 116, Issue 1

Article
JACOBIAN ELLIPTIC FUNCTIONS IN SIGNATURE FOUR
P. L. ROBINSON
Bulletin of the Australian Mathematical Society, Volume 109, Issue 1

Article
ON THE NUMBER OF ALGEBRAIC POINTS ON THE GRAPH OF THE WEIERSTRASS SIGMA FUNCTIONS
GOREKH PRASAD SENA, K. SENTHIL KUMAR
Bulletin of the Australian Mathematical Society, Volume 108, Issue 2

Article
Effective rigid analytic trivializations for Drinfeld modules
Chalinee Khaochim, Matthew A. Papanikolas
Canadian Journal of Mathematics, Volume 75, Issue 3

Article
A restaurant process with cocktail bar and relations to the three-parameter Mittag–Leffler distribution
Martin Möhle
Journal of Applied Probability, Volume 58, Issue 4

Article
On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative
Anh Tuan Nguyen, Tomás Caraballo, Nguyen Huy Tuan
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, Volume 152, Issue 4

Article
q-DISCRETE PAINLEVÉ EQUATIONS: THEIR HIERARCHIES AND PROPERTIES
HUDA DAEFALLH ALRASHDI
Bulletin of the Australian Mathematical Society, Volume 103, Issue 2

Article
ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION
LAURENT BÉTERMIN
Bulletin of the Australian Mathematical Society, Volume 102, Issue 1

Article
ON GUILLERA’S ${}_{7}F_{6}( \frac {27}{64} )$-SERIES FOR ${1}/{\pi ^2}$
JOHN M. CAMPBELL
Bulletin of the Australian Mathematical Society, Volume 108, Issue 3

Article
APÉRY LIMITS FOR ELLIPTIC $\boldsymbol {L}$ -VALUES
CHRISTOPH KOUTSCHAN, WADIM ZUDILIN
Bulletin of the Australian Mathematical Society, Volume 106, Issue 2

Article
AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS
SAIEI-JAEYEONG MATSUBARA-HEO, NOBUKI TAKAYAMA
Nagoya Mathematical Journal, Volume 246

Article
A MAGNETIC DOUBLE INTEGRAL
DAVID BROADHURST, WADIM ZUDILIN
Journal of the Australian Mathematical Society, Volume 107, Issue 1

Article
Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations
Liming Liao, Guanghua Ji, Zhongwei Tang, Hui Zhang
East Asian Journal on Applied Mathematics, Volume 7, Issue 3

Article
Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
Yonggui Yan, Zhi-Zhong Sun, Jiwei Zhang
Communications in Computational Physics, Volume 22, Issue 4

Article
Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
Shidong Jiang, Jiwei Zhang, Qian Zhang, Zhimin Zhang
Communications in Computational Physics, Volume 21, Issue 3

Article
RANDOM WALKS, ELLIPTIC INTEGRALS AND RELATED CONSTANTS
JAMES GU FENG WAN
Bulletin of the Australian Mathematical Society, Volume 89, Issue 1

MSC 2010: Special functions

Special functions (33-XX)

Elementary classical functions (33Bxx)

A DYNAMICAL SYSTEM PROOF OF NIVEN’S THEOREM AND ITS EXTENSIONS

On two congruence conjectures of Z.-W. Sun involving Franel numbers

On the distribution of the digits of quotients of integers and primes

Cotangent Sums Related to the Riemann Hypothesis for Various Shifts of the Argument

SYMMETRIC FUNCTIONS AND MULTIPLE ZETA VALUES

ON THE ACCURACY OF ASYMPTOTIC APPROXIMATIONS TO THE LOG-GAMMA AND RIEMANN–SIEGEL THETA FUNCTIONS

SUPERCONGRUENCES INVOLVING $p$-ADIC GAMMA FUNCTIONS

INEQUALITIES ASSOCIATED WITH RATIOS OF GAMMA FUNCTIONS

Hypergeometric functions (33Cxx)

Basic hypergeometric functions (33Dxx)

NEW CONGRUENCES FOR THE TRUNCATED APPELL SERIES $F_1$

New mock theta functions and formulas for basic hypergeometric series

A $\boldsymbol {q}$ -SUPERCONGRUENCE MODULO THE THIRD POWER OF A CYCLOTOMIC POLYNOMIAL

A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES $\boldsymbol F_3$

A NEW $\boldsymbol {q}$ -ANALOGUE OF VAN HAMME’S (A.2) SUPERCONGRUENCE

NEW GENERALISATIONS OF VAN HAMME’S (G.2) SUPERCONGRUENCE

A FAMILY OF $\boldsymbol {q}$ -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL

Inverse K-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type

Other special functions (33Exx)

GHOSTS AND CONGRUENCES FOR $\boldsymbol {p}^{\boldsymbol {s}}$-APPROXIMATIONS OF HYPERGEOMETRIC PERIODS

JACOBIAN ELLIPTIC FUNCTIONS IN SIGNATURE FOUR

ON THE NUMBER OF ALGEBRAIC POINTS ON THE GRAPH OF THE WEIERSTRASS SIGMA FUNCTIONS

Effective rigid analytic trivializations for Drinfeld modules

A restaurant process with cocktail bar and relations to the three-parameter Mittag–Leffler distribution

On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative

q-DISCRETE PAINLEVÉ EQUATIONS: THEIR HIERARCHIES AND PROPERTIES

ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION

Computational aspects (33Fxx)

ON GUILLERA’S ${}_{7}F_{6}( \frac {27}{64} )$-SERIES FOR ${1}/{\pi ^2}$

APÉRY LIMITS FOR ELLIPTIC $\boldsymbol {L}$ -VALUES

AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS

A MAGNETIC DOUBLE INTEGRAL

Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations

Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme

Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations

RANDOM WALKS, ELLIPTIC INTEGRALS AND RELATED CONSTANTS