Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a837)

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.a837.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(3/2), 17/4}, -z] == (1/(901943132160 z^(13/4))) (13 (Sqrt[Pi] (51326611875 + 33617430000 z + 21515155200 z^2 + 52157952000 z^3 - 39739392000 z^4 + 18166579200 z^5 + 8808038400 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-51326611875 + 21130956000 z + 439084800 z^2 - 2069544960 z^3 + 681246720 z^4 + 534773760 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (17108870625 + 3384612000 z + 3313094400 z^2 - 2513387520 z^3 + 1039073280 z^4 + 547356672 z^5 + 16777216 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]