Apéry's constant: Difference between revisions

Line 489:

Last digit of the 1000 terms line is 2 under pwa/p2js...

As per Wren, you can verify or completely replace all this with mpfr_zeta_ui(w,3) [on desktop/Phix only, not supported under pwa/p2js]

=={{header|Python}}==

from sympy import zeta, factorial

from decimal import Decimal, getcontext

# Set the desired precision

getcontext().prec = 120

def my_sympy_format_to_decimal(sympy_result):

return Decimal(str(sympy_result.evalf(getcontext().prec)))

def print_apery_constant(description, value):

print(f"{description}:\n{str(value)[:102]}")

# Apéry's constant via SymPy's zeta function

zeta_3_str = str(zeta(3).evalf(getcontext().prec))

zeta_3_decimal = Decimal(zeta_3_str)

print_apery_constant("Apéry's constant via SymPy's zeta", zeta_3_decimal)

# Apéry's constant via Riemann summation of 1/(k cubed)

def apery_r(nterms=1_000):

total = sum(Decimal('1') / Decimal(k) ** 3 for k in range(1, nterms + 1))

return total

print_apery_constant("Apéry's constant via reciprocal cubes", apery_r())

# Apéry's constant via Markov's summation

def apery_m(nterms=158):

total = Decimal(2.5) * sum(

(Decimal(1) if k % 2 != 0 else Decimal(-1)) *

my_sympy_format_to_decimal(factorial(k) ** 2) /

my_sympy_format_to_decimal(factorial(2*k) * (k ** 3) )

for k in range(1, nterms + 1)

)

return total

print_apery_constant("Apéry's constant via Markov's summation", apery_m())

# Apéry's constant via Wedeniwski's summation

def apery_w(nterms=20):

total = Decimal('1') / Decimal('24') * sum(

(Decimal('1') if k % 2 == 0 else Decimal('-1')) *

my_sympy_format_to_decimal(factorial(2 * k + 1)) ** 3 *

my_sympy_format_to_decimal(factorial(2 * k)) ** 3 *

my_sympy_format_to_decimal(factorial(k)) ** 3 *

(Decimal('126392') * Decimal(k) ** 5 +

Decimal('412708') * Decimal(k) ** 4 +

Decimal('531578') * Decimal(k) ** 3 +

Decimal('336367') * Decimal(k) ** 2 +

Decimal('104000') * Decimal(k) +

Decimal('12463')) /

(my_sympy_format_to_decimal(factorial(3 * k + 2)) * my_sympy_format_to_decimal(factorial(4 * k + 3)) ** 3)

for k in range(0, nterms + 1)

)

return total

print_apery_constant("Apéry's constant via Wedeniwski's summation", apery_w())

</syntaxhighlight>

<pre>

Apéry's constant via SymPy's zeta:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

Apéry's constant via reciprocal cubes:

1.2020564036593442854830714115115999903483212709031775135036540966118572571921400836130084123260473111

Apéry's constant via Markov's summation:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

Apéry's constant via Wedeniwski's summation:

1.2020569031595942853997381615114499907649862923404988817922715553418382057863130901864558736093352581

</pre>

=={{header|Raku}}==