<\/a>Features<\/h2>\n\n\n\n- Algebra<\/a><\/li>
- Arithmetic<\/a><\/li>
- Finance<\/a><\/li>
- Functions
- Map<\/a><\/li>
- Special Functions<\/a><\/li><\/ul><\/li>
- Information Theory
- Entropy<\/a><\/li><\/ul><\/li>
- Linear Algebra
- Matrix<\/a><\/li>
- Vector<\/a><\/li><\/ul><\/li>
- Numbers
- Complex<\/a><\/li>
- Rational<\/a><\/li><\/ul><\/li>
- Number Theory
- Integers<\/a><\/li><\/ul><\/li>
- Numerical Analysis
- Interpolation<\/a><\/li>
- Numerical Differentiation<\/a><\/li>
- Numerical Integration<\/a><\/li>
- Root Finding<\/a><\/li><\/ul><\/li>
- Probability
- Combinatorics<\/a><\/li>
- Distributions
- Continuous<\/a><\/li>
- Discrete<\/a><\/li>
- Multivariate<\/a><\/li>
- Tables<\/a><\/li><\/ul><\/li><\/ul><\/li>
- Sequences
- Basic<\/a><\/li>
- Advanced<\/a><\/li><\/ul><\/li>
- Set Theory<\/a><\/li>
- Statistics
- ANOVA<\/a><\/li>
- Averages<\/a><\/li>
- Circular<\/a><\/li>
- Correlation<\/a><\/li>
- Descriptive<\/a><\/li>
- Distance and Divergence<\/a><\/li>
- Distributions<\/a><\/li>
- Effect Size<\/a><\/li>
- Experiments<\/a><\/li>
- Kernel Density Estimation<\/a><\/li>
- Random Variables<\/a><\/li>
- Regressions<\/a><\/li>
- Significance Testing<\/a><\/li><\/ul><\/li>
- Trigonometry<\/a><\/li><\/ul>\n\n\n\n
<\/a>Setup<\/h2>\n\n\n\nAdd the library to your composer.json<\/code> file in your project:<\/p>\n\n\n\n{\n \"require\": {\n \"markrogoyski\/math-php\": \"0.*\"\n }\n}<\/pre>\n\n\n\nUse composer<\/a> to install the library:<\/p>\n\n\n\n$ php composer.phar install<\/pre>\n\n\n\nComposer will install MathPHP inside your vendor folder. Then you can add the following to your .php files to use the library with Autoloading.<\/p>\n\n\n\n
require_once(__DIR__ . '\/vendor\/autoload.php');<\/pre>\n\n\n\nAlternatively, use composer on the command line to require and install MathPHP:<\/p>\n\n\n\n
$ php composer.phar require markrogoyski\/math-php:0.*\n<\/code><\/pre>\n\n\n\n<\/a>Minimum Requirements<\/h3>\n\n\n\n- PHP 7<\/li><\/ul>\n\n\n\n
<\/a>Usage<\/h2>\n\n\n\n<\/a>Algebra<\/h3>\n\n\n\nuse MathPHP\\Algebra;\n\n\/\/<\/em> Greatest common divisor (GCD)<\/em>\n$gcd = Algebra::gcd(8, 12);\n\n\/\/<\/em> Extended greatest common divisor - gcd(a, b) = a*a' + b*b'<\/em>\n$gcd = Algebra::extendedGcd(12, 8); \/\/<\/em> returns array [gcd, a', b']<\/em>\n\n\/\/<\/em> Least common multiple (LCM)<\/em>\n$lcm = Algebra::lcm(5, 2);\n\n\/\/<\/em> Factors of an integer<\/em>\n$factors = Algebra::factors(12); \/\/<\/em> returns [1, 2, 3, 4, 6, 12]<\/em>\n\n\/\/<\/em> Quadradic equation<\/em>\nlist($a, $b, $c) = [1, 2, -8]; \/\/<\/em> x\u00b2 + 2x - 8<\/em>\nlist($x\u2081, $x\u2082) = Algebra::quadradic($a, $b, $c);\n\n\/\/<\/em> Cubic equation<\/em>\nlist($a\u2083, $a\u2082, $a\u2081, $a\u2080) = [2, 9, 3, -4]; \/\/<\/em> 2x\u00b3 + 9x\u00b2 + 3x -4<\/em>\nlist($x\u2081, $x\u2082, $x\u2083) = Algebra::cubic($a\u2083, $a\u2082, $a\u2081, $a\u2080);\n\n\/\/<\/em> Quartic equation<\/em>\nlist($a\u2084, $a\u2083, $a\u2082, $a\u2081, $a\u2080) = [1, -10, 35, -50, 24]; \/\/<\/em> z\u2074 - 10z\u00b3 + 35z\u00b2 - 50z + 24 = 0<\/em>\nlist($z\u2081, $z\u2082, $z\u2083, $z\u2084) = Algebra::quartic($a\u2084, $a\u2083, $a\u2082, $a\u2081, $a\u2080);<\/pre>\n\n\n\n<\/a>Arithmetic<\/h3>\n\n\n\nuse MathPHP\\Arithmetic;\n\n$\u00b3\u221ax = Arithmetic::cubeRoot(-8); \/\/<\/em> -2<\/em>\n\n\/\/<\/em> Sum of digits<\/em>\n$digit_sum = Arithmetic::digitSum(99): \/\/<\/em> 18<\/em>\n$digital_root = Arithmetic::digitalRoot(99); \/\/<\/em> 9<\/em>\n\n\/\/<\/em> Equality of numbers within a tolerance<\/em>\n$x = 0.00000003458;\n$y = 0.00000003455;\n$\u03b5 = 0.0000000001;\n$almostEqual = Arithmetic::almostEqual($x, $y, $\u03b5); \/\/<\/em> true<\/em>\n\n\/\/<\/em> Copy sign<\/em>\n$magnitude = 5;\n$sign = -3;\n$signed_magnitude = Arithmetic::copySign($magnitude, $sign); \/\/<\/em> -5<\/em><\/pre>\n\n\n\n<\/a>Finance<\/h3>\n\n\n\nuse MathPHP\\Finance;\n\n\/\/<\/em> Financial payment for a loan or annuity with compound interest<\/em>\n$rate = 0.035 \/ 12; \/\/<\/em> 3.5\n$periods = 30 * 12; \/\/<\/em> 30-year mortgage<\/em>\n$present_value = 265000; \/\/<\/em> Mortgage note of $265,000.00<\/em>\n$future_value = 0;\n$beginning = false; \/\/<\/em> Adjust the payment to the beginning or end of the period<\/em>\n$pmt = Finance::pmt($rate, $periods, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Interest on a financial payment for a loan or annuity with compound interest.<\/em>\n$period = 1; \/\/<\/em> First payment period<\/em>\n$ipmt = Finance::ipmt($rate, $period, $periods, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Principle on a financial payment for a loan or annuity with compound interest<\/em>\n$ppmt = Finance::ppmt($rate, $period, $periods, $present_value, $future_value = 0, $beginning);\n\n\/\/<\/em> Number of payment periods of an annuity.<\/em>\n$periods = Finance::periods($rate, $payment, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Annual Equivalent Rate (AER) of an annual percentage rate (APR)<\/em>\n$nominal = 0.035; \/\/<\/em> APR 3.5\n$periods = 12; \/\/<\/em> Compounded monthly<\/em>\n$aer = Finance::aer($nominal, $periods);\n\n\/\/<\/em> Annual nominal rate of an annual effective rate (AER)<\/em>\n$nomial = Finance::nominal($aer, $periods);\n\n\/\/<\/em> Future value for a loan or annuity with compound interest<\/em>\n$payment = 1189.97;\n$fv = Finance::fv($rate, $periods, $payment, $present_value, $beginning)\n\n\/\/<\/em> Present value for a loan or annuity with compound interest<\/em>\n$pv = Finance::pv($rate, $periods, $payment, $future_value, $beginning)\n\n\/\/<\/em> Net present value of cash flows<\/em>\n$values = [-1000, 100, 200, 300, 400];\n$npv = Finance::npv($rate, $values);\n\n\/\/<\/em> Interest rate per period of an annuity<\/em>\n$beginning = false; \/\/<\/em> Adjust the payment to the beginning or end of the period<\/em>\n$rate = rate($periods, $payment, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Internal rate of return<\/em>\n$values = [-100, 50, 40, 30];\n$irr = Finance:irr($values); \/\/<\/em> Rate of return of an initial investment of $100 with returns of $50, $40, and $30<\/em>\n\n\/\/<\/em> Modified internal rate of return<\/em>\n$finance_rate = 0.05; \/\/<\/em> 5\n$reinvestment_rate = 0.10; \/\/<\/em> reinvested at 10\n$mirr = Finance:mirr($values, $finance_rate); \/\/<\/em> rate of return of an initial investment of $100 at 5\n\n\/\/<\/em> Discounted payback of an investment<\/em>\n$values = [-1000, 100, 200, 300, 400, 500];\n$rate = 0.1;\n$payback = Finance::payback($values, $rate); \/\/<\/em> The payback period of an investment with a $1,000 investment and future returns of $100, $200, $300, $400, $500 and a discount rate of 0.10<\/em>\n\n\/\/<\/em> Profitability index<\/em>\n$values = [-100, 50, 50, 50];\n$profitability_index = profitabilityIndex($values, $rate); \/\/<\/em> The profitability index of an initial $100 investment with future returns of $50, $50, $50 with a 10\n\n\n\n<\/a>Functions – Map – Single Array<\/h3>\n\n\n\nuse MathPHP\\Functions\\Map;\n\n$x = [1, 2, 3, 4];\n\n$sums = Map\\Single::add($x, 2); \/\/ [3, 4, 5, 6]\n$differences = Map\\Single::subtract($x, 1); \/\/ [0, 1, 2, 3]\n$products = Map\\Single::multiply($x, 5); \/\/ [5, 10, 15, 20]\n$quotients = Map\\Single::divide($x, 2); \/\/ [0.5, 1, 1.5, 2]\n$x\u00b2 = Map\\Single::square($x); \/\/ [1, 4, 9, 16]\n$x\u00b3 = Map\\Single::cube($x); \/\/ [1, 8, 27, 64]\n$x\u2074 = Map\\Single::pow($x, 4); \/\/ [1, 16, 81, 256]\n$\u221ax = Map\\Single::sqrt($x); \/\/ [1, 1.414, 1.732, 2]\n$\u2223x\u2223 = Map\\Single::abs($x); \/\/ [1, 2, 3, 4]\n$maxes = Map\\Single::max($x, 3); \/\/ [3, 3, 3, 4]\n$mins = Map\\Single::min($x, 3); \/\/ [1, 2, 3, 3]<\/pre>\n\n\n\n<\/a>Functions – Map – Multiple Arrays<\/h3>\n\n\n\nuse MathPHP\\Functions\\Map;\n\n$x = [10, 10, 10, 10];\n$y = [1, 2, 5, 10];\n\n\/\/<\/em> Map function against elements of two or more arrays, item by item (by item ...)<\/em>\n$sums = Map\\Multi::add($x, $y); \/\/<\/em> [11, 12, 15, 20]<\/em>\n$differences = Map\\Multi::subtract($x, $y); \/\/<\/em> [9, 8, 5, 0]<\/em>\n$products = Map\\Multi::multiply($x, $y); \/\/<\/em> [10, 20, 50, 100]<\/em>\n$quotients = Map\\Multi::divide($x, $y); \/\/<\/em> [10, 5, 2, 1]<\/em>\n$maxes = Map\\Multi::max($x, $y); \/\/<\/em> [10, 10, 10, 10]<\/em>\n$mins = Map\\Multi::mins($x, $y); \/\/<\/em> [1, 2, 5, 10]<\/em>\n\n\/\/<\/em> All functions work on multiple arrays; not limited to just two<\/em>\n$x = [10, 10, 10, 10];\n$y = [1, 2, 5, 10];\n$z = [4, 5, 6, 7];\n$sums = Map\\Multi::add($x, $y, $z); \/\/<\/em> [15, 17, 21, 27]<\/em><\/pre>\n\n\n\n<\/a>Functions – Special Functions<\/h3>\n\n\n\nuse MathPHP\\Functions\\Special;\n\n\/\/<\/em>
- Map<\/a><\/li>
- Special Functions<\/a><\/li><\/ul><\/li>
- Information Theory
- Entropy<\/a><\/li><\/ul><\/li>
- Linear Algebra
- Matrix<\/a><\/li>
- Vector<\/a><\/li><\/ul><\/li>
- Numbers
- Complex<\/a><\/li>
- Rational<\/a><\/li><\/ul><\/li>
- Number Theory
- Integers<\/a><\/li><\/ul><\/li>
- Numerical Analysis
- Interpolation<\/a><\/li>
- Numerical Differentiation<\/a><\/li>
- Numerical Integration<\/a><\/li>
- Root Finding<\/a><\/li><\/ul><\/li>
- Probability
- Combinatorics<\/a><\/li>
- Distributions
- Continuous<\/a><\/li>
- Discrete<\/a><\/li>
- Multivariate<\/a><\/li>
- Tables<\/a><\/li><\/ul><\/li><\/ul><\/li>
- Sequences
- Basic<\/a><\/li>
- Advanced<\/a><\/li><\/ul><\/li>
- Set Theory<\/a><\/li>
- Statistics
- ANOVA<\/a><\/li>
- Averages<\/a><\/li>
- Circular<\/a><\/li>
- Correlation<\/a><\/li>
- Descriptive<\/a><\/li>
- Distance and Divergence<\/a><\/li>
- Distributions<\/a><\/li>
- Effect Size<\/a><\/li>
- Experiments<\/a><\/li>
- Kernel Density Estimation<\/a><\/li>
- Random Variables<\/a><\/li>
- Regressions<\/a><\/li>
- Significance Testing<\/a><\/li><\/ul><\/li>
- Trigonometry<\/a><\/li><\/ul>\n\n\n\n
<\/a>Setup<\/h2>\n\n\n\n
Add the library to your
composer.json<\/code> file in your project:<\/p>\n\n\n\n{\n \"require\": {\n \"markrogoyski\/math-php\": \"0.*\"\n }\n}<\/pre>\n\n\n\nUse composer<\/a> to install the library:<\/p>\n\n\n\n
$ php composer.phar install<\/pre>\n\n\n\n
Composer will install MathPHP inside your vendor folder. Then you can add the following to your .php files to use the library with Autoloading.<\/p>\n\n\n\n
require_once(__DIR__ . '\/vendor\/autoload.php');<\/pre>\n\n\n\n
Alternatively, use composer on the command line to require and install MathPHP:<\/p>\n\n\n\n
$ php composer.phar require markrogoyski\/math-php:0.*\n<\/code><\/pre>\n\n\n\n<\/a>Minimum Requirements<\/h3>\n\n\n\n
- PHP 7<\/li><\/ul>\n\n\n\n
<\/a>Usage<\/h2>\n\n\n\n
<\/a>Algebra<\/h3>\n\n\n\n
use MathPHP\\Algebra;\n\n\/\/<\/em> Greatest common divisor (GCD)<\/em>\n$gcd = Algebra::gcd(8, 12);\n\n\/\/<\/em> Extended greatest common divisor - gcd(a, b) = a*a' + b*b'<\/em>\n$gcd = Algebra::extendedGcd(12, 8); \/\/<\/em> returns array [gcd, a', b']<\/em>\n\n\/\/<\/em> Least common multiple (LCM)<\/em>\n$lcm = Algebra::lcm(5, 2);\n\n\/\/<\/em> Factors of an integer<\/em>\n$factors = Algebra::factors(12); \/\/<\/em> returns [1, 2, 3, 4, 6, 12]<\/em>\n\n\/\/<\/em> Quadradic equation<\/em>\nlist($a, $b, $c) = [1, 2, -8]; \/\/<\/em> x\u00b2 + 2x - 8<\/em>\nlist($x\u2081, $x\u2082) = Algebra::quadradic($a, $b, $c);\n\n\/\/<\/em> Cubic equation<\/em>\nlist($a\u2083, $a\u2082, $a\u2081, $a\u2080) = [2, 9, 3, -4]; \/\/<\/em> 2x\u00b3 + 9x\u00b2 + 3x -4<\/em>\nlist($x\u2081, $x\u2082, $x\u2083) = Algebra::cubic($a\u2083, $a\u2082, $a\u2081, $a\u2080);\n\n\/\/<\/em> Quartic equation<\/em>\nlist($a\u2084, $a\u2083, $a\u2082, $a\u2081, $a\u2080) = [1, -10, 35, -50, 24]; \/\/<\/em> z\u2074 - 10z\u00b3 + 35z\u00b2 - 50z + 24 = 0<\/em>\nlist($z\u2081, $z\u2082, $z\u2083, $z\u2084) = Algebra::quartic($a\u2084, $a\u2083, $a\u2082, $a\u2081, $a\u2080);<\/pre>\n\n\n\n
<\/a>Arithmetic<\/h3>\n\n\n\n
use MathPHP\\Arithmetic;\n\n$\u00b3\u221ax = Arithmetic::cubeRoot(-8); \/\/<\/em> -2<\/em>\n\n\/\/<\/em> Sum of digits<\/em>\n$digit_sum = Arithmetic::digitSum(99): \/\/<\/em> 18<\/em>\n$digital_root = Arithmetic::digitalRoot(99); \/\/<\/em> 9<\/em>\n\n\/\/<\/em> Equality of numbers within a tolerance<\/em>\n$x = 0.00000003458;\n$y = 0.00000003455;\n$\u03b5 = 0.0000000001;\n$almostEqual = Arithmetic::almostEqual($x, $y, $\u03b5); \/\/<\/em> true<\/em>\n\n\/\/<\/em> Copy sign<\/em>\n$magnitude = 5;\n$sign = -3;\n$signed_magnitude = Arithmetic::copySign($magnitude, $sign); \/\/<\/em> -5<\/em><\/pre>\n\n\n\n
<\/a>Finance<\/h3>\n\n\n\n
use MathPHP\\Finance;\n\n\/\/<\/em> Financial payment for a loan or annuity with compound interest<\/em>\n$rate = 0.035 \/ 12; \/\/<\/em> 3.5\n$periods = 30 * 12; \/\/<\/em> 30-year mortgage<\/em>\n$present_value = 265000; \/\/<\/em> Mortgage note of $265,000.00<\/em>\n$future_value = 0;\n$beginning = false; \/\/<\/em> Adjust the payment to the beginning or end of the period<\/em>\n$pmt = Finance::pmt($rate, $periods, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Interest on a financial payment for a loan or annuity with compound interest.<\/em>\n$period = 1; \/\/<\/em> First payment period<\/em>\n$ipmt = Finance::ipmt($rate, $period, $periods, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Principle on a financial payment for a loan or annuity with compound interest<\/em>\n$ppmt = Finance::ppmt($rate, $period, $periods, $present_value, $future_value = 0, $beginning);\n\n\/\/<\/em> Number of payment periods of an annuity.<\/em>\n$periods = Finance::periods($rate, $payment, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Annual Equivalent Rate (AER) of an annual percentage rate (APR)<\/em>\n$nominal = 0.035; \/\/<\/em> APR 3.5\n$periods = 12; \/\/<\/em> Compounded monthly<\/em>\n$aer = Finance::aer($nominal, $periods);\n\n\/\/<\/em> Annual nominal rate of an annual effective rate (AER)<\/em>\n$nomial = Finance::nominal($aer, $periods);\n\n\/\/<\/em> Future value for a loan or annuity with compound interest<\/em>\n$payment = 1189.97;\n$fv = Finance::fv($rate, $periods, $payment, $present_value, $beginning)\n\n\/\/<\/em> Present value for a loan or annuity with compound interest<\/em>\n$pv = Finance::pv($rate, $periods, $payment, $future_value, $beginning)\n\n\/\/<\/em> Net present value of cash flows<\/em>\n$values = [-1000, 100, 200, 300, 400];\n$npv = Finance::npv($rate, $values);\n\n\/\/<\/em> Interest rate per period of an annuity<\/em>\n$beginning = false; \/\/<\/em> Adjust the payment to the beginning or end of the period<\/em>\n$rate = rate($periods, $payment, $present_value, $future_value, $beginning);\n\n\/\/<\/em> Internal rate of return<\/em>\n$values = [-100, 50, 40, 30];\n$irr = Finance:irr($values); \/\/<\/em> Rate of return of an initial investment of $100 with returns of $50, $40, and $30<\/em>\n\n\/\/<\/em> Modified internal rate of return<\/em>\n$finance_rate = 0.05; \/\/<\/em> 5\n$reinvestment_rate = 0.10; \/\/<\/em> reinvested at 10\n$mirr = Finance:mirr($values, $finance_rate); \/\/<\/em> rate of return of an initial investment of $100 at 5\n\n\/\/<\/em> Discounted payback of an investment<\/em>\n$values = [-1000, 100, 200, 300, 400, 500];\n$rate = 0.1;\n$payback = Finance::payback($values, $rate); \/\/<\/em> The payback period of an investment with a $1,000 investment and future returns of $100, $200, $300, $400, $500 and a discount rate of 0.10<\/em>\n\n\/\/<\/em> Profitability index<\/em>\n$values = [-100, 50, 50, 50];\n$profitability_index = profitabilityIndex($values, $rate); \/\/<\/em> The profitability index of an initial $100 investment with future returns of $50, $50, $50 with a 10\n\n\n\n
<\/a>Functions – Map – Single Array<\/h3>\n\n\n\n
use MathPHP\\Functions\\Map;\n\n$x = [1, 2, 3, 4];\n\n$sums = Map\\Single::add($x, 2); \/\/ [3, 4, 5, 6]\n$differences = Map\\Single::subtract($x, 1); \/\/ [0, 1, 2, 3]\n$products = Map\\Single::multiply($x, 5); \/\/ [5, 10, 15, 20]\n$quotients = Map\\Single::divide($x, 2); \/\/ [0.5, 1, 1.5, 2]\n$x\u00b2 = Map\\Single::square($x); \/\/ [1, 4, 9, 16]\n$x\u00b3 = Map\\Single::cube($x); \/\/ [1, 8, 27, 64]\n$x\u2074 = Map\\Single::pow($x, 4); \/\/ [1, 16, 81, 256]\n$\u221ax = Map\\Single::sqrt($x); \/\/ [1, 1.414, 1.732, 2]\n$\u2223x\u2223 = Map\\Single::abs($x); \/\/ [1, 2, 3, 4]\n$maxes = Map\\Single::max($x, 3); \/\/ [3, 3, 3, 4]\n$mins = Map\\Single::min($x, 3); \/\/ [1, 2, 3, 3]<\/pre>\n\n\n\n
<\/a>Functions – Map – Multiple Arrays<\/h3>\n\n\n\n
use MathPHP\\Functions\\Map;\n\n$x = [10, 10, 10, 10];\n$y = [1, 2, 5, 10];\n\n\/\/<\/em> Map function against elements of two or more arrays, item by item (by item ...)<\/em>\n$sums = Map\\Multi::add($x, $y); \/\/<\/em> [11, 12, 15, 20]<\/em>\n$differences = Map\\Multi::subtract($x, $y); \/\/<\/em> [9, 8, 5, 0]<\/em>\n$products = Map\\Multi::multiply($x, $y); \/\/<\/em> [10, 20, 50, 100]<\/em>\n$quotients = Map\\Multi::divide($x, $y); \/\/<\/em> [10, 5, 2, 1]<\/em>\n$maxes = Map\\Multi::max($x, $y); \/\/<\/em> [10, 10, 10, 10]<\/em>\n$mins = Map\\Multi::mins($x, $y); \/\/<\/em> [1, 2, 5, 10]<\/em>\n\n\/\/<\/em> All functions work on multiple arrays; not limited to just two<\/em>\n$x = [10, 10, 10, 10];\n$y = [1, 2, 5, 10];\n$z = [4, 5, 6, 7];\n$sums = Map\\Multi::add($x, $y, $z); \/\/<\/em> [15, 17, 21, 27]<\/em><\/pre>\n\n\n\n
<\/a>Functions – Special Functions<\/h3>\n\n\n\n
use MathPHP\\Functions\\Special;\n\n\/\/<\/em>
- Averages<\/a><\/li>
- Advanced<\/a><\/li><\/ul><\/li>
- Discrete<\/a><\/li>
- Distributions
- Numerical Differentiation<\/a><\/li>
- Numerical Analysis
- Rational<\/a><\/li><\/ul><\/li>
- Vector<\/a><\/li><\/ul><\/li>
- Linear Algebra
- Special Functions<\/a><\/li><\/ul><\/li>