Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9905)

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`=-3/2

http://functions.wolfram.com/07.22.03.9905.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(3/2), 15/4}, -z] == (11 (Sqrt[Pi] (-43616234025 - 41050573200 z - 50523782400 z^2 + 149700096000 z^3 - 95808061440 z^4 + 102195265536 z^5 + 13975420928 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-14538744675 - 7037241120 z + 11400963840 z^2 - 6869925888 z^3 + 6230310912 z^4 + 870318080 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (43616234025 - 5473409760 z + 18552119040 z^2 - 9305210880 z^3 + 5630263296 z^4 + 857735168 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(2029372047360 z^(11/4))

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]