Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a87b)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a87b.01

Input Form

HypergeometricPFQ[{-(15/4)}, {3/2, 21/4}, -z] == (Sqrt[Pi] (-4656674397375 - 4168212048000 z - 3705077376000 z^2 - 7904165068800 z^3 + 158083301376000 z^4 + 134897750507520 z^5 + 17129873080320 z^6 + 547608330240 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((4656674397375 - 798907309200 z + 520475155200 z^2 + 4940103168000 z^3 + 7544889999360 z^4 + 1039521546240 z^5 + 33973862400 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-1552224799125 - 679815536400 z - 714550636800 z^2 + 8659937341440 z^3 + 8243725271040 z^4 + 1064309882880 z^5 + 34175188992 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (173173081374720 z^(17/4))

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]