Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8756)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8756.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 19/4}, z] == (-4 z^(1/4) (-2327405863808025 - 3103207818410700 Sqrt[z] - 1031715846120960 z + 515857923060480 z^(3/2) + 136791456721920 z^2 - 385328047104000 z^(5/2) + 237124952064000 z^3 - 602416528293888 z^(7/2) + 123066674970624 z^4 - 367412161019904 z^(9/2) + 80781691060224 z^5 - 366133597175808 z^(11/2) - 16095457050624 z^6 + 65999688695808 z^(13/2) + 554050781184 z^7 - 2229088026624 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (2327405863808025 - 3103207818410700 Sqrt[z] + 1031715846120960 z + 515857923060480 z^(3/2) - 136791456721920 z^2 - 385328047104000 z^(5/2) - 237124952064000 z^3 - 602416528293888 z^(7/2) - 123066674970624 z^4 - 367412161019904 z^(9/2) - 80781691060224 z^5 - 366133597175808 z^(11/2) + 16095457050624 z^6 + 65999688695808 z^(13/2) - 554050781184 z^7 - 2229088026624 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (2327405863808025 - 1450850408607600 z + 780289295385600 z^2 - 746943599001600 z^3 - 1991849597337600 z^4 - 1274783742296064 z^5 - 1510854805684224 z^6 + 265644800999424 z^7 - 8929237008384 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (2327405863808025 - 1450850408607600 z + 780289295385600 z^2 - 746943599001600 z^3 - 1991849597337600 z^4 - 1274783742296064 z^5 - 1510854805684224 z^6 + 265644800999424 z^7 - 8929237008384 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (9974769487183872 z^(15/4))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]