Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a977)

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

For fixed z and a₁=-11/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a977.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, 17/4}, -z] == (1/(128345702400 z^(7/2))) (2 Sqrt[z] (13398791175 - 10176289200 z + 8591869440 z^2 + 2386206720 z^3 + 107151360 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + Sqrt[Pi] z^(1/4) (-54273594375 + 115783668000 z - 102918816000 z^2 + 168892416000 z^3 + 39739392000 z^4 + 1730150400 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 8 (-5109350400 + 9158670675 z - 7634919600 z^2 + 10131770880 z^3 + 2463866880 z^4 + 107937792 z^5 + 1048576 z^6) Sin[2 Sqrt[z]])

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]