Inheritance diagram for SymEngine::PolyGamma:

Collaboration diagram for SymEngine::PolyGamma:

Public Member Functions
void	accept (Visitor &v) const override

void	accept (EvalRealDoubleVisitorFinal &v) const override

	PolyGamma (const RCP< const Basic > &n, const RCP< const Basic > &x)
	PolyGamma Constructor.

bool	is_canonical (const RCP< const Basic > &n, const RCP< const Basic > &x)

RCP< const Basic >	rewrite_as_zeta () const

RCP< const Basic >	create (const RCP< const Basic > &a, const RCP< const Basic > &b) const override

virtual RCP< const Basic >	create (const RCP< const Basic > &a, const RCP< const Basic > &b) const=0

RCP< const Basic >	create (const vec_basic &b) const

Public Member Functions inherited from SymEngine::TwoArgBasic< BaseClass >
	TwoArgBasic (const RCP< const Basic > &a, const RCP< const Basic > &b)
	`b` in `TwoArgBasic(a, b)`

hash_t	__hash__ () const override

RCP< const Basic >	get_arg1 () const

RCP< const Basic >	get_arg2 () const

vec_basic	get_args () const override

virtual RCP< const Basic >	create (const RCP< const Basic > &a, const RCP< const Basic > &b) const =0
	Method to construct classes with canonicalization.

RCP< const Basic >	create (const vec_basic &b) const

bool	__eq__ (const Basic &o) const override

int	compare (const Basic &o) const override
	Structural equality comparator.

Static Public Attributes
static const TypeID	type_code_id = SYMENGINE_POLYGAMMA

Detailed Description

Definition at line 1204 of file functions.h.

Constructor & Destructor Documentation

◆ PolyGamma()

SymEngine::PolyGamma::PolyGamma	(	const RCP< const Basic > &	n,
		const RCP< const Basic > &	x
	)

inline

PolyGamma Constructor.

Definition at line 1220 of file functions.h.

        : TwoArgFunction(n, x)
    {
        SYMENGINE_ASSIGN_TYPEID()
        SYMENGINE_ASSERT(is_canonical(n, x))
    }

Member Function Documentation

◆ create() [1/3]

RCP< const Basic > SymEngine::PolyGamma::create	(	const RCP< const Basic > &	a,
		const RCP< const Basic > &	b
	)		const

overridevirtual

Returns: canonicalized PolyGamma

Implements SymEngine::TwoArgBasic< BaseClass >.

Definition at line 3391 of file functions.cpp.

{
    return polygamma(a, b);
}

◆ create() [2/3]

virtual RCP< const Basic > SymEngine::TwoArgBasic< BaseClass >::create	(	const RCP< const Basic > &	a,
		const RCP< const Basic > &	b
	)		const

virtual

The polygamma function

It is a meromorphic function on \mathbb{C} and defined as the (n+1)-th derivative of the logarithm of the gamma function:

.. math:: \psi^{(n)} (z) := \frac{\mathrm{d}^{n+1}}{\mathrm{d} z^{n+1}} \log\Gamma(z).

Implements SymEngine::TwoArgBasic< BaseClass >.

◆ create() [3/3]

RCP< const Basic > SymEngine::TwoArgBasic< BaseClass >::create ( const vec_basic & b ) const

inline

The polygamma function

It is a meromorphic function on \mathbb{C} and defined as the (n+1)-th derivative of the logarithm of the gamma function:

.. math:: \psi^{(n)} (z) := \frac{\mathrm{d}^{n+1}}{\mathrm{d} z^{n+1}} \log\Gamma(z).

Definition at line 108 of file functions.h.

    {
        SYMENGINE_ASSERT(b.size() == 2);
        return create(b[0], b[1]);
    }

◆ is_canonical()

bool SymEngine::PolyGamma::is_canonical	(	const RCP< const Basic > &	n,
		const RCP< const Basic > &	x
	)

Definition at line 3354 of file functions.cpp.

{
    if (is_a_Number(*x) and not(down_cast<const Number &>(*x)).is_positive()) {
        return false;
    }
    if (eq(*n, *zero)) {
        if (eq(*x, *one)) {
            return false;
        }
        if (is_a<Rational>(*x)) {
            auto x_ = rcp_static_cast<const Rational>(x);
            auto den = get_den(x_->as_rational_class());
            if (den == 2 or den == 3 or den == 4) {
                return false;
            }
        }
    }
    return true;
}

◆ rewrite_as_zeta()

RCP< const Basic > SymEngine::PolyGamma::rewrite_as_zeta ( ) const

Definition at line 3375 of file functions.cpp.

{
    if (not is_a<Integer>(*get_arg1())) {
        return rcp_from_this();
    }
    RCP<const Integer> n = rcp_static_cast<const Integer>(get_arg1());
    if (not(n->is_positive())) {
        return rcp_from_this();
    }
    if ((n->as_int() & 1) == 0) {
        return neg(mul(factorial(n->as_int()), zeta(add(n, one), get_arg2())));
    } else {
        return mul(factorial(n->as_int()), zeta(add(n, one), get_arg2()));
    }
}

Field Documentation

◆ type_code_id

const TypeID SymEngine::PolyGamma::type_code_id = SYMENGINE_POLYGAMMA

static

Type_code_id shared by all instances

Definition at line 1218 of file functions.h.

The documentation for this class was generated from the following files:

/home/runner/work/symengine/symengine/symengine/functions.h
/home/runner/work/symengine/symengine/symengine/functions.cpp

Public Member Functions

Static Public Attributes