Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9765)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9765.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(9/2), 19/4}, -z] == (11 (Sqrt[Pi] (-11478702389529375 - 4047586517520000 z - 1116575591040000 z^2 - 476405585510400 z^3 + 453719605248000 z^4 - 68324834672640 z^5 + 4671783567360 z^6 - 182536110080 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-3826234129843125 + 399940096374000 z - 38105357472000 z^2 + 29315172741120 z^3 - 4330410147840 z^4 + 294235668480 z^5 - 11458838528 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (11478702389529375 - 8196362697978000 z - 91275623712000 z^2 + 33956258918400 z^3 - 4595009126400 z^4 + 303672852480 z^5 - 11660165120 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (8312307905986560 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]