Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8757)

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/07.22.03.8757.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 19/4}, -z] == (Sqrt[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) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-775801954602675 - 128964480765120 z - 96332011776000 z^2 + 150604132073472 z^3 - 91853040254976 z^4 + 91533399293952 z^5 + 16499922173952 z^6 + 557272006656 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (2327405863808025 - 1031715846120960 z - 136791456721920 z^2 + 237124952064000 z^3 - 123066674970624 z^4 + 80781691060224 z^5 + 16095457050624 z^6 + 554050781184 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(2493692371795968 z^(15/4))

Standard Form

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MathML Form

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Rule 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]